diff --git a/package-lock.json b/package-lock.json
index 331257edb56d..266b5cf89701 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1546,6 +1546,55 @@
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         "wide-align": {
           "version": "1.1.2",
-          "resolved": "https://registry.npmjs.org/wide-align/-/wide-align-1.1.2.tgz",
+          "resolved": false,
           "integrity": "sha512-ijDLlyQ7s6x1JgCLur53osjm/UXUYD9+0PbYKrBsYisYXzCxN+HC3mYDNy/dWdmf3AwqwU3CXwDCvsNgGK1S0w==",
           "dev": true,
           "requires": {
@@ -9166,7 +9224,7 @@
         },
         "wrappy": {
           "version": "1.0.2",
-          "resolved": "https://registry.npmjs.org/wrappy/-/wrappy-1.0.2.tgz",
+          "resolved": false,
           "integrity": "sha1-tSQ9jz7BqjXxNkYFvA0QNuMKtp8=",
           "dev": true
         }
@@ -11567,7 +11625,7 @@
     },
     "json5": {
       "version": "0.5.1",
-      "resolved": "http://registry.npmjs.org/json5/-/json5-0.5.1.tgz",
+      "resolved": "https://registry.npmjs.org/json5/-/json5-0.5.1.tgz",
       "integrity": "sha1-Hq3nrMASA0rYTiOWdn6tn6VJWCE=",
       "dev": true
     },
diff --git a/package.json b/package.json
index 91792d7d9631..67add648aedc 100644
--- a/package.json
+++ b/package.json
@@ -61,6 +61,7 @@
     "@types/fs-extra": "^4.0.3",
     "@types/glob": "^5.0.33",
     "@types/gulp": "3.8.32",
+    "@types/gulp-util": "^3.0.34",
     "@types/hammerjs": "^2.0.35",
     "@types/jasmine": "^2.8.8",
     "@types/merge2": "^0.3.30",
diff --git a/src/cdk-experimental/dialog/dialog-injectors.ts b/src/cdk-experimental/dialog/dialog-injectors.ts
index ec9d4c513a1d..443455c41efb 100644
--- a/src/cdk-experimental/dialog/dialog-injectors.ts
+++ b/src/cdk-experimental/dialog/dialog-injectors.ts
@@ -7,7 +7,11 @@
  */
 
 import {InjectionToken} from '@angular/core';
-import {ComponentType, Overlay, ScrollStrategy, BlockScrollStrategy} from '@angular/cdk/overlay';
+import {
+  ComponentType,
+  Overlay,
+  ScrollStrategy,
+} from '@angular/cdk/overlay';
 import {DialogRef} from './dialog-ref';
 import {CdkDialogContainer} from './dialog-container';
 import {DialogConfig} from './dialog-config';
@@ -31,7 +35,7 @@ export const DIALOG_CONTAINER =
 
 /** @docs-private */
 export function MAT_DIALOG_SCROLL_STRATEGY_PROVIDER_FACTORY(overlay: Overlay):
-    () => BlockScrollStrategy {
+    () => ScrollStrategy {
   return () => overlay.scrollStrategies.block();
 }
 
diff --git a/src/cdk-experimental/dialog/dialog.ts b/src/cdk-experimental/dialog/dialog.ts
index f2673b8507f9..1699f2caba8b 100644
--- a/src/cdk-experimental/dialog/dialog.ts
+++ b/src/cdk-experimental/dialog/dialog.ts
@@ -14,7 +14,8 @@ import {
   Injector,
   Inject,
   ComponentRef,
-  OnDestroy
+  OnDestroy,
+  Type
 } from '@angular/core';
 import {ComponentPortal, PortalInjector, TemplatePortal} from '@angular/cdk/portal';
 import {of as observableOf, Observable, Subject, defer} from 'rxjs';
@@ -28,6 +29,7 @@ import {
   Overlay,
   OverlayRef,
   OverlayConfig,
+  ScrollStrategy,
 } from '@angular/cdk/overlay';
 import {startWith} from 'rxjs/operators';
 
@@ -45,6 +47,8 @@ import {
  */
 @Injectable()
 export class Dialog implements OnDestroy {
+  private _scrollStrategy: () => ScrollStrategy;
+
   /** Stream that emits when all dialogs are closed. */
   get _afterAllClosed(): Observable<void> {
     return this._parentDialog ? this._parentDialog.afterAllClosed : this._afterAllClosedBase;
@@ -68,8 +72,10 @@ export class Dialog implements OnDestroy {
   constructor(
       private overlay: Overlay,
       private injector: Injector,
-      @Inject(DIALOG_REF) private dialogRefConstructor,
-      @Inject(DIALOG_SCROLL_STRATEGY) private _scrollStrategy,
+      @Inject(DIALOG_REF) private dialogRefConstructor: Type<DialogRef<any>>,
+      // TODO(crisbeto): the `any` here can be replaced
+      // with the proper type once we start using Ivy.
+      @Inject(DIALOG_SCROLL_STRATEGY) scrollStrategy: any,
       @Optional() @SkipSelf() private _parentDialog: Dialog,
       @Optional() location: Location) {
 
@@ -79,6 +85,8 @@ export class Dialog implements OnDestroy {
     if (!_parentDialog && location) {
       location.subscribe(() => this.closeAll());
     }
+
+    this._scrollStrategy = scrollStrategy;
   }
 
   /** Gets an open dialog by id. */
diff --git a/src/cdk-experimental/tsconfig-build.json b/src/cdk-experimental/tsconfig-build.json
index e3cb4e371ee1..c0029abe6b90 100644
--- a/src/cdk-experimental/tsconfig-build.json
+++ b/src/cdk-experimental/tsconfig-build.json
@@ -8,6 +8,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "importHelpers": true,
     "newLine": "lf",
     "module": "es2015",
diff --git a/src/cdk/accordion/accordion.spec.ts b/src/cdk/accordion/accordion.spec.ts
index 7af1185d3f1b..e5e613742048 100644
--- a/src/cdk/accordion/accordion.spec.ts
+++ b/src/cdk/accordion/accordion.spec.ts
@@ -66,12 +66,10 @@ describe('CdkAccordion', () => {
 
 @Component({template: `
   <cdk-accordion [multi]="multi">
-    <cdk-accordion-item #item1></cdk-accordion-item>
-    <cdk-accordion-item #item2></cdk-accordion-item>
+    <cdk-accordion-item></cdk-accordion-item>
+    <cdk-accordion-item></cdk-accordion-item>
   </cdk-accordion>`})
 class SetOfItems {
-  @ViewChild('item1') item1;
-  @ViewChild('item2') item2;
   multi: boolean = false;
 }
 
diff --git a/src/cdk/collections/tree-adapter.ts b/src/cdk/collections/tree-adapter.ts
index abbab2fceaa1..f718f11b9837 100644
--- a/src/cdk/collections/tree-adapter.ts
+++ b/src/cdk/collections/tree-adapter.ts
@@ -27,5 +27,5 @@ export interface TreeDataNodeFlattener<T> {
    * Put node descendants of node in array.
    * If `onlyExpandable` is true, then only process expandable descendants.
    */
-  nodeDescendents(node: T, nodes: T[], onlyExpandable: boolean);
+  nodeDescendents(node: T, nodes: T[], onlyExpandable: boolean): void;
 }
diff --git a/src/cdk/drag-drop/drag-utils.spec.ts b/src/cdk/drag-drop/drag-utils.spec.ts
index 47f9982823fe..e54d3bf31535 100644
--- a/src/cdk/drag-drop/drag-utils.spec.ts
+++ b/src/cdk/drag-drop/drag-utils.spec.ts
@@ -57,7 +57,7 @@ describe('dragging utilities', () => {
     });
 
     it('should not do anything if the source array is empty', () => {
-      const a = [];
+      const a: number[] = [];
       const b = [3, 4, 5];
 
       transferArrayItem(a, b, 0, 0);
diff --git a/src/cdk/drag-drop/drag.ts b/src/cdk/drag-drop/drag.ts
index 571bbbd152eb..fe2c2cb02630 100644
--- a/src/cdk/drag-drop/drag.ts
+++ b/src/cdk/drag-drop/drag.ts
@@ -28,7 +28,7 @@ import {
   SkipSelf,
   ViewContainerRef,
 } from '@angular/core';
-import {Observable, Subject, Subscription} from 'rxjs';
+import {Observable, Subject, Subscription, Observer} from 'rxjs';
 import {take} from 'rxjs/operators';
 import {DragDropRegistry} from './drag-drop-registry';
 import {
@@ -206,15 +206,16 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
    * Emits as the user is dragging the item. Use with caution,
    * because this event will fire for every pixel that the user has dragged.
    */
-  @Output('cdkDragMoved') moved: Observable<CdkDragMove<T>> = Observable.create(observer => {
-    const subscription = this._moveEvents.subscribe(observer);
-    this._moveEventSubscriptions++;
-
-    return () => {
-      subscription.unsubscribe();
-      this._moveEventSubscriptions--;
-    };
-  });
+  @Output('cdkDragMoved') moved: Observable<CdkDragMove<T>> =
+      Observable.create((observer: Observer<CdkDragMove<T>>) => {
+        const subscription = this._moveEvents.subscribe(observer);
+        this._moveEventSubscriptions++;
+
+        return () => {
+          subscription.unsubscribe();
+          this._moveEventSubscriptions--;
+        };
+      });
 
   constructor(
     /** Element that the draggable is attached to. */
@@ -470,7 +471,7 @@ export class CdkDrag<T = any> implements AfterViewInit, OnDestroy {
    * Updates the item's position in its drop container, or moves it
    * into a new one, depending on its current drag position.
    */
-  private _updateActiveDropContainer({x, y}) {
+  private _updateActiveDropContainer({x, y}: Point) {
     // Drop container that draggable has been moved into.
     let newContainer = this.dropContainer._getSiblingContainerFromPosition(this, x, y);
 
diff --git a/src/cdk/layout/breakpoints-observer.spec.ts b/src/cdk/layout/breakpoints-observer.spec.ts
index 4f67427602f5..a80f207029f6 100644
--- a/src/cdk/layout/breakpoints-observer.spec.ts
+++ b/src/cdk/layout/breakpoints-observer.spec.ts
@@ -137,7 +137,7 @@ export class FakeMediaQueryList {
   /** The callback for change events. */
   addListenerCallback?: (mql: MediaQueryListEvent) => void;
 
-  constructor(public matches, public media) {}
+  constructor(public matches: boolean, public media: string) {}
 
   /** Toggles the matches state and "emits" a change event. */
   setMatches(matches: boolean) {
diff --git a/src/cdk/layout/breakpoints-observer.ts b/src/cdk/layout/breakpoints-observer.ts
index 13dfe1c7cf0d..a7cab7f42bdb 100644
--- a/src/cdk/layout/breakpoints-observer.ts
+++ b/src/cdk/layout/breakpoints-observer.ts
@@ -98,7 +98,10 @@ export class BreakpointObserver implements OnDestroy {
     }
 
     const mql: MediaQueryList = this.mediaMatcher.matchMedia(query);
-    let queryListener;
+
+    // TODO(jelbourn): change this `any` to `MediaQueryListEvent` once Google has upgraded to
+    // TypeScript 3.1 (the type is unavailable before then).
+    let queryListener: any;
 
     // Create callback for match changes and add it is as a listener.
     const queryObservable = fromEventPattern<MediaQueryList>(
@@ -108,8 +111,6 @@ export class BreakpointObserver implements OnDestroy {
       // have MediaQueryList inherit from EventTarget, which causes inconsistencies in how Zone.js
       // patches it.
       (listener: Function) => {
-        // TODO(jelbourn): change this `any` to `MediaQueryListEvent` once Google has upgraded to
-        // TypeScript 3.1 (the type is unavailable before then).
         queryListener = (e: any) => this.zone.run(() => listener(e));
         mql.addListener(queryListener);
       },
diff --git a/src/cdk/observers/observe-content.ts b/src/cdk/observers/observe-content.ts
index baef9349ac45..f9d91c44fe24 100644
--- a/src/cdk/observers/observe-content.ts
+++ b/src/cdk/observers/observe-content.ts
@@ -19,7 +19,7 @@ import {
   OnDestroy,
   Output,
 } from '@angular/core';
-import {Observable, Subject, Subscription} from 'rxjs';
+import {Observable, Subject, Subscription, Observer} from 'rxjs';
 import {debounceTime} from 'rxjs/operators';
 
 /**
@@ -65,7 +65,7 @@ export class ContentObserver implements OnDestroy {
   observe(elementOrRef: Element | ElementRef<Element>): Observable<MutationRecord[]> {
     const element = elementOrRef instanceof ElementRef ? elementOrRef.nativeElement : elementOrRef;
 
-    return Observable.create(observer => {
+    return Observable.create((observer: Observer<MutationRecord[]>) => {
       const stream = this._observeElement(element);
       const subscription = stream.subscribe(observer);
 
diff --git a/src/cdk/overlay/overlay-config.ts b/src/cdk/overlay/overlay-config.ts
index aa19e1958c26..08f985163b60 100644
--- a/src/cdk/overlay/overlay-config.ts
+++ b/src/cdk/overlay/overlay-config.ts
@@ -8,8 +8,7 @@
 
 import {PositionStrategy} from './position/position-strategy';
 import {Direction, Directionality} from '@angular/cdk/bidi';
-import {ScrollStrategy} from './scroll/scroll-strategy';
-import {NoopScrollStrategy} from './scroll/noop-scroll-strategy';
+import {ScrollStrategy, NoopScrollStrategy} from './scroll/index';
 
 
 /** Initial configuration used when creating an overlay. */
@@ -62,9 +61,13 @@ export class OverlayConfig {
 
   constructor(config?: OverlayConfig) {
     if (config) {
-      Object.keys(config)
-        .filter(key => typeof config[key] !== 'undefined')
-        .forEach(key => this[key] = config[key]);
+      Object.keys(config).forEach(k => {
+        const key = k as keyof OverlayConfig;
+
+        if (typeof config[key] !== 'undefined') {
+          this[key] = config[key];
+        }
+      });
     }
   }
 }
diff --git a/src/cdk/overlay/overlay-directives.ts b/src/cdk/overlay/overlay-directives.ts
index 7252f8493a56..ef51ee15c6e7 100644
--- a/src/cdk/overlay/overlay-directives.ts
+++ b/src/cdk/overlay/overlay-directives.ts
@@ -114,6 +114,7 @@ export class CdkConnectedOverlay implements OnDestroy, OnChanges {
   private _offsetX: number;
   private _offsetY: number;
   private _position: FlexibleConnectedPositionStrategy;
+  private _scrollStrategyFactory: () => ScrollStrategy;
 
   /** Origin for the connected overlay. */
   @Input('cdkConnectedOverlayOrigin') origin: CdkOverlayOrigin;
@@ -165,8 +166,7 @@ export class CdkConnectedOverlay implements OnDestroy, OnChanges {
   @Input('cdkConnectedOverlayViewportMargin') viewportMargin: number = 0;
 
   /** Strategy to be used when handling scroll events while the overlay is open. */
-  @Input('cdkConnectedOverlayScrollStrategy') scrollStrategy: ScrollStrategy =
-      this._scrollStrategy();
+  @Input('cdkConnectedOverlayScrollStrategy') scrollStrategy: ScrollStrategy;
 
   /** Whether the overlay is open. */
   @Input('cdkConnectedOverlayOpen') open: boolean = false;
@@ -219,9 +219,11 @@ export class CdkConnectedOverlay implements OnDestroy, OnChanges {
       private _overlay: Overlay,
       templateRef: TemplateRef<any>,
       viewContainerRef: ViewContainerRef,
-      @Inject(CDK_CONNECTED_OVERLAY_SCROLL_STRATEGY) private _scrollStrategy,
+      @Inject(CDK_CONNECTED_OVERLAY_SCROLL_STRATEGY) scrollStrategyFactory: any,
       @Optional() private _dir: Directionality) {
     this._templatePortal = new TemplatePortal(templateRef, viewContainerRef);
+    this._scrollStrategyFactory = scrollStrategyFactory;
+    this.scrollStrategy = this._scrollStrategyFactory();
   }
 
   /** The associated overlay reference. */
diff --git a/src/cdk/overlay/overlay-ref.ts b/src/cdk/overlay/overlay-ref.ts
index 61a5066a46ee..2a7d1c5a1241 100644
--- a/src/cdk/overlay/overlay-ref.ts
+++ b/src/cdk/overlay/overlay-ref.ts
@@ -10,7 +10,7 @@ import {Direction, Directionality} from '@angular/cdk/bidi';
 import {ComponentPortal, Portal, PortalOutlet, TemplatePortal} from '@angular/cdk/portal';
 import {ComponentRef, EmbeddedViewRef, NgZone} from '@angular/core';
 import {Location} from '@angular/common';
-import {Observable, Subject, merge, SubscriptionLike, Subscription} from 'rxjs';
+import {Observable, Subject, merge, SubscriptionLike, Subscription, Observer} from 'rxjs';
 import {take, takeUntil} from 'rxjs/operators';
 import {OverlayKeyboardDispatcher} from './keyboard/overlay-keyboard-dispatcher';
 import {OverlayConfig} from './overlay-config';
@@ -42,15 +42,16 @@ export class OverlayRef implements PortalOutlet, OverlayReference {
    */
   private _previousHostParent: HTMLElement;
 
-  private _keydownEventsObservable: Observable<KeyboardEvent> = Observable.create(observer => {
-    const subscription = this._keydownEvents.subscribe(observer);
-    this._keydownEventSubscriptions++;
+  private _keydownEventsObservable: Observable<KeyboardEvent> =
+      Observable.create((observer: Observer<KeyboardEvent>) => {
+        const subscription = this._keydownEvents.subscribe(observer);
+        this._keydownEventSubscriptions++;
 
-    return () => {
-      subscription.unsubscribe();
-      this._keydownEventSubscriptions--;
-    };
-  });
+        return () => {
+          subscription.unsubscribe();
+          this._keydownEventSubscriptions--;
+        };
+      });
 
   /** Stream of keydown events dispatched to this overlay. */
   _keydownEvents = new Subject<KeyboardEvent>();
diff --git a/src/cdk/overlay/position/flexible-connected-position-strategy.ts b/src/cdk/overlay/position/flexible-connected-position-strategy.ts
index 690517fe38ab..2e9fd387cba2 100644
--- a/src/cdk/overlay/position/flexible-connected-position-strategy.ts
+++ b/src/cdk/overlay/position/flexible-connected-position-strategy.ts
@@ -16,7 +16,7 @@ import {
   validateHorizontalPosition,
   validateVerticalPosition,
 } from './connected-position';
-import {Observable, Subscription, Subject} from 'rxjs';
+import {Observable, Subscription, Subject, Observer} from 'rxjs';
 import {OverlayReference} from '../overlay-reference';
 import {isElementScrolledOutsideView, isElementClippedByScrolling} from './scroll-clip';
 import {coerceCssPixelValue, coerceArray} from '@angular/cdk/coercion';
@@ -122,15 +122,16 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
   private _previousPushAmount: {x: number, y: number} | null;
 
   /** Observable sequence of position changes. */
-  positionChanges: Observable<ConnectedOverlayPositionChange> = Observable.create(observer => {
-    const subscription = this._positionChanges.subscribe(observer);
-    this._positionChangeSubscriptions++;
-
-    return () => {
-      subscription.unsubscribe();
-      this._positionChangeSubscriptions--;
-    };
-  });
+  positionChanges: Observable<ConnectedOverlayPositionChange> =
+      Observable.create((observer: Observer<ConnectedOverlayPositionChange>) => {
+        const subscription = this._positionChanges.subscribe(observer);
+        this._positionChangeSubscriptions++;
+
+        return () => {
+          subscription.unsubscribe();
+          this._positionChangeSubscriptions--;
+        };
+      });
 
   /** Ordered list of preferred positions, from most to least desirable. */
   get positions() {
@@ -705,7 +706,7 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
   private _calculateBoundingBoxRect(origin: Point, position: ConnectedPosition): BoundingBoxRect {
     const viewport = this._viewportRect;
     const isRtl = this._isRtl();
-    let height, top, bottom;
+    let height: number, top: number, bottom: number;
 
     if (position.overlayY === 'top') {
       // Overlay is opening "downward" and thus is bound by the bottom viewport edge.
@@ -745,7 +746,7 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
         (position.overlayX === 'end' && !isRtl) ||
         (position.overlayX === 'start' && isRtl);
 
-    let width, left, right;
+    let width: number, left: number, right: number;
 
     if (isBoundedByLeftViewportEdge) {
       right = viewport.right - origin.x + this._viewportMargin;
@@ -770,7 +771,7 @@ export class FlexibleConnectedPositionStrategy implements PositionStrategy {
       }
     }
 
-    return {top, left, bottom, right, width, height};
+    return {top: top!, left: left!, bottom: bottom!, right: right!, width, height};
   }
 
   /**
diff --git a/src/cdk/overlay/scroll/block-scroll-strategy.spec.ts b/src/cdk/overlay/scroll/block-scroll-strategy.spec.ts
index b21dac77df52..c4970763eee3 100644
--- a/src/cdk/overlay/scroll/block-scroll-strategy.spec.ts
+++ b/src/cdk/overlay/scroll/block-scroll-strategy.spec.ts
@@ -144,22 +144,24 @@ describe('BlockScrollStrategy', () => {
   it('should not clobber user-defined scroll-behavior', skipIOS(() => {
     const root = documentElement;
     const body = document.body;
+    const rootStyle = root.style as CSSStyleDeclaration & {scrollBehavior: string};
+    const bodyStyle = body.style as CSSStyleDeclaration & {scrollBehavior: string};
 
-    root.style['scrollBehavior'] = body.style['scrollBehavior'] = 'smooth';
+    rootStyle.scrollBehavior = bodyStyle.scrollBehavior = 'smooth';
 
     // Get the value via the style declaration in order to
     // handle browsers that don't support the property yet.
-    const initialRootValue = root.style['scrollBehavior'];
-    const initialBodyValue = root.style['scrollBehavior'];
+    const initialRootValue = rootStyle.scrollBehavior;
+    const initialBodyValue = rootStyle.scrollBehavior;
 
     overlayRef.attach(componentPortal);
     overlayRef.detach();
 
-    expect(root.style['scrollBehavior']).toBe(initialRootValue);
-    expect(body.style['scrollBehavior']).toBe(initialBodyValue);
+    expect(rootStyle.scrollBehavior).toBe(initialRootValue);
+    expect(bodyStyle.scrollBehavior).toBe(initialBodyValue);
 
     // Avoid bleeding styles into other tests.
-    root.style['scrollBehavior'] = body.style['scrollBehavior'] = '';
+    rootStyle.scrollBehavior = bodyStyle.scrollBehavior = '';
   }));
 
   /**
diff --git a/src/cdk/overlay/scroll/block-scroll-strategy.ts b/src/cdk/overlay/scroll/block-scroll-strategy.ts
index 28ba51691630..65c625f8b6e9 100644
--- a/src/cdk/overlay/scroll/block-scroll-strategy.ts
+++ b/src/cdk/overlay/scroll/block-scroll-strategy.ts
@@ -10,11 +10,18 @@ import {ScrollStrategy} from './scroll-strategy';
 import {ViewportRuler} from '@angular/cdk/scrolling';
 import {coerceCssPixelValue} from '@angular/cdk/coercion';
 
+/**
+ * Extended `CSSStyleDeclaration` that includes `scrollBehavior` which isn't part of the
+ * built-in TS typings. Once it is, this declaration can be removed safely.
+ * @docs-private
+ */
+type ScrollBehaviorCSSStyleDeclaration = CSSStyleDeclaration & {scrollBehavior: string};
+
 /**
  * Strategy that will prevent the user from scrolling while the overlay is visible.
  */
 export class BlockScrollStrategy implements ScrollStrategy {
-  private _previousHTMLStyles = { top: '', left: '' };
+  private _previousHTMLStyles = {top: '', left: ''};
   private _previousScrollPosition: { top: number, left: number };
   private _isEnabled = false;
   private _document: Document;
@@ -51,23 +58,25 @@ export class BlockScrollStrategy implements ScrollStrategy {
     if (this._isEnabled) {
       const html = this._document.documentElement!;
       const body = this._document.body!;
-      const previousHtmlScrollBehavior = html.style['scrollBehavior'] || '';
-      const previousBodyScrollBehavior = body.style['scrollBehavior'] || '';
+      const htmlStyle = html.style as ScrollBehaviorCSSStyleDeclaration;
+      const bodyStyle = body.style as ScrollBehaviorCSSStyleDeclaration;
+      const previousHtmlScrollBehavior = htmlStyle.scrollBehavior || '';
+      const previousBodyScrollBehavior = bodyStyle.scrollBehavior || '';
 
       this._isEnabled = false;
 
-      html.style.left = this._previousHTMLStyles.left;
-      html.style.top = this._previousHTMLStyles.top;
+      htmlStyle.left = this._previousHTMLStyles.left;
+      htmlStyle.top = this._previousHTMLStyles.top;
       html.classList.remove('cdk-global-scrollblock');
 
       // Disable user-defined smooth scrolling temporarily while we restore the scroll position.
       // See https://developer.mozilla.org/en-US/docs/Web/CSS/scroll-behavior
-      html.style['scrollBehavior'] = body.style['scrollBehavior'] = 'auto';
+      htmlStyle.scrollBehavior = bodyStyle.scrollBehavior = 'auto';
 
       window.scroll(this._previousScrollPosition.left, this._previousScrollPosition.top);
 
-      html.style['scrollBehavior'] = previousHtmlScrollBehavior;
-      body.style['scrollBehavior'] = previousBodyScrollBehavior;
+      htmlStyle.scrollBehavior = previousHtmlScrollBehavior;
+      bodyStyle.scrollBehavior = previousBodyScrollBehavior;
     }
   }
 
diff --git a/src/cdk/scrolling/scroll-dispatcher.ts b/src/cdk/scrolling/scroll-dispatcher.ts
index 9af317c31e06..99ab18927d51 100644
--- a/src/cdk/scrolling/scroll-dispatcher.ts
+++ b/src/cdk/scrolling/scroll-dispatcher.ts
@@ -15,7 +15,7 @@ import {
   Optional,
   SkipSelf,
 } from '@angular/core';
-import {fromEvent, of as observableOf, Subject, Subscription, Observable} from 'rxjs';
+import {fromEvent, of as observableOf, Subject, Subscription, Observable, Observer} from 'rxjs';
 import {auditTime, filter} from 'rxjs/operators';
 import {CdkScrollable} from './scrollable';
 
@@ -82,7 +82,11 @@ export class ScrollDispatcher implements OnDestroy {
    * to run the callback using `NgZone.run`.
    */
   scrolled(auditTimeInMs: number = DEFAULT_SCROLL_TIME): Observable<CdkScrollable|void> {
-    return this._platform.isBrowser ? Observable.create(observer => {
+    if (!this._platform.isBrowser) {
+      return observableOf<void>();
+    }
+
+    return Observable.create((observer: Observer<CdkScrollable|void>) => {
       if (!this._globalSubscription) {
         this._addGlobalListener();
       }
@@ -103,7 +107,7 @@ export class ScrollDispatcher implements OnDestroy {
           this._removeGlobalListener();
         }
       };
-    }) : observableOf<void>();
+    });
   }
 
   ngOnDestroy() {
diff --git a/src/cdk/scrolling/scrollable.ts b/src/cdk/scrolling/scrollable.ts
index 645491b78fcb..0b404a1a998a 100644
--- a/src/cdk/scrolling/scrollable.ts
+++ b/src/cdk/scrolling/scrollable.ts
@@ -13,7 +13,7 @@ import {
   supportsScrollBehavior
 } from '@angular/cdk/platform';
 import {Directive, ElementRef, NgZone, OnDestroy, OnInit, Optional} from '@angular/core';
-import {fromEvent, Observable, Subject} from 'rxjs';
+import {fromEvent, Observable, Subject, Observer} from 'rxjs';
 import {takeUntil} from 'rxjs/operators';
 import {ScrollDispatcher} from './scroll-dispatcher';
 
@@ -47,7 +47,7 @@ export type ExtendedScrollToOptions = _XAxis & _YAxis & ScrollOptions;
 export class CdkScrollable implements OnInit, OnDestroy {
   private _destroyed = new Subject();
 
-  private _elementScrolled: Observable<Event> = Observable.create(observer =>
+  private _elementScrolled: Observable<Event> = Observable.create((observer: Observer<Event>) =>
       this.ngZone.runOutsideAngular(() =>
           fromEvent(this.elementRef.nativeElement, 'scroll').pipe(takeUntil(this._destroyed))
               .subscribe(observer)));
diff --git a/src/cdk/scrolling/virtual-scroll-strategy.ts b/src/cdk/scrolling/virtual-scroll-strategy.ts
index f5bee1630c76..cd7f0cb569be 100644
--- a/src/cdk/scrolling/virtual-scroll-strategy.ts
+++ b/src/cdk/scrolling/virtual-scroll-strategy.ts
@@ -31,16 +31,16 @@ export interface VirtualScrollStrategy {
   detach(): void;
 
   /** Called when the viewport is scrolled (debounced using requestAnimationFrame). */
-  onContentScrolled();
+  onContentScrolled(): void;
 
   /** Called when the length of the data changes. */
-  onDataLengthChanged();
+  onDataLengthChanged(): void;
 
   /** Called when the range of items rendered in the DOM has changed. */
-  onContentRendered();
+  onContentRendered(): void;
 
   /** Called when the offset of the rendered items changed. */
-  onRenderedOffsetChanged();
+  onRenderedOffsetChanged(): void;
 
   /**
    * Scroll to the offset for the given index.
diff --git a/src/cdk/scrolling/virtual-scroll-viewport.ts b/src/cdk/scrolling/virtual-scroll-viewport.ts
index da9014da345e..4207ea2756b5 100644
--- a/src/cdk/scrolling/virtual-scroll-viewport.ts
+++ b/src/cdk/scrolling/virtual-scroll-viewport.ts
@@ -23,7 +23,7 @@ import {
   ViewChild,
   ViewEncapsulation,
 } from '@angular/core';
-import {animationFrameScheduler, Observable, Subject} from 'rxjs';
+import {animationFrameScheduler, Observable, Subject, Observer} from 'rxjs';
 import {auditTime, startWith, takeUntil} from 'rxjs/operators';
 import {ScrollDispatcher} from './scroll-dispatcher';
 import {CdkScrollable, ExtendedScrollToOptions} from './scrollable';
@@ -66,9 +66,10 @@ export class CdkVirtualScrollViewport extends CdkScrollable implements OnInit, O
   // depending on how the strategy calculates the scrolled index, it may come at a cost to
   // performance.
   /** Emits when the index of the first element visible in the viewport changes. */
-  @Output() scrolledIndexChange: Observable<number> = Observable.create(observer =>
-      this._scrollStrategy.scrolledIndexChange.subscribe(index =>
-          Promise.resolve().then(() => this.ngZone.run(() => observer.next(index)))));
+  @Output() scrolledIndexChange: Observable<number> =
+      Observable.create((observer: Observer<number>) =>
+        this._scrollStrategy.scrolledIndexChange.subscribe(index =>
+            Promise.resolve().then(() => this.ngZone.run(() => observer.next(index)))));
 
   /** The element that wraps the rendered content. */
   @ViewChild('contentWrapper') _contentWrapper: ElementRef<HTMLElement>;
diff --git a/src/cdk/table/table.spec.ts b/src/cdk/table/table.spec.ts
index 18259a2f097f..7bab50b5a2a6 100644
--- a/src/cdk/table/table.spec.ts
+++ b/src/cdk/table/table.spec.ts
@@ -708,6 +708,7 @@ describe('CdkTable', () => {
 
   describe('with sticky positioning', () => {
     interface PositionDirections {
+      [key: string]: string | undefined;
       top?: string;
       bottom?: string;
       left?: string;
@@ -731,21 +732,23 @@ describe('CdkTable', () => {
       expect(element.style.zIndex).toBe(zIndex, `Expected zIndex to be ${zIndex}`);
 
       ['top', 'bottom', 'left', 'right'].forEach(d => {
-        if (!directions[d]) {
+        const directionValue = directions[d];
+
+        if (!directionValue) {
           // If no expected position for this direction, must either be unset or empty string
           expect(element.style[d] || 'unset').toBe('unset', `Expected ${d} to be unset`);
           return;
         }
 
-        const expectationMessage = `Expected direction ${d} to be ${directions[d]}`;
+        const expectationMessage = `Expected direction ${d} to be ${directionValue}`;
 
         // If the direction contains `px`, we parse the number to be able to avoid deviations
         // caused by individual browsers.
-        if (directions[d].includes('px')) {
+        if (directionValue.includes('px')) {
           expect(Math.round(parseInt(element.style[d])))
-            .toBe(Math.round(parseInt(directions[d])), expectationMessage);
+            .toBe(Math.round(parseInt(directionValue)), expectationMessage);
         } else {
-          expect(element.style[d]).toBe(directions[d], expectationMessage);
+          expect(element.style[d]).toBe(directionValue, expectationMessage);
         }
       });
     }
@@ -1095,7 +1098,7 @@ describe('CdkTable', () => {
   });
 
   describe('with trackBy', () => {
-    function createTestComponentWithTrackyByTable(trackByStrategy) {
+    function createTestComponentWithTrackyByTable(trackByStrategy: string) {
       fixture = createComponent(TrackByCdkTableApp);
 
       component = fixture.componentInstance;
@@ -1150,7 +1153,7 @@ describe('CdkTable', () => {
 
       // Change each item reference to show that the trackby is not checking the item properties.
       component.dataSource.data = component.dataSource.data
-          .map(item => { return {a: item.a, b: item.b, c: item.c}; });
+          .map((item: TestData) => ({a: item.a, b: item.b, c: item.c}));
 
       // Expect that all the rows are considered new since their references are all different
       const changedRows = getRows(tableElement);
@@ -1167,7 +1170,7 @@ describe('CdkTable', () => {
       // Change each item reference to show that the trackby is checking the item properties.
       // Otherwise this would cause them all to be removed/added.
       component.dataSource.data = component.dataSource.data
-          .map(item => { return {a: item.a, b: item.b, c: item.c}; });
+          .map((item: TestData) => ({a: item.a, b: item.b, c: item.c}));
 
       // Expect that the first and second rows were swapped and that the last row is new
       const changedRows = getRows(tableElement);
@@ -1184,7 +1187,7 @@ describe('CdkTable', () => {
       // Change each item reference to show that the trackby is checking the index.
       // Otherwise this would cause them all to be removed/added.
       component.dataSource.data = component.dataSource.data
-          .map(item => { return {a: item.a, b: item.b, c: item.c}; });
+          .map((item: TestData) => ({a: item.a, b: item.b, c: item.c}));
 
       // Expect first two to be the same since they were swapped but indicies are consistent.
       // The third element was removed and caught by the table so it was removed before another
@@ -1206,7 +1209,7 @@ describe('CdkTable', () => {
       // Change each item reference to show that the trackby is checking the index.
       // Otherwise this would cause them all to be removed/added.
       component.dataSource.data = component.dataSource.data
-          .map(item => ({a: item.a, b: item.b, c: item.c}));
+          .map((item: TestData) => ({a: item.a, b: item.b, c: item.c}));
 
       // Expect the rows were given the right implicit data even though the rows were not moved.
       fixture.detectChanges();
@@ -2043,7 +2046,7 @@ class MissingFooterRowDefCdkTableApp {
   `
 })
 class UndefinedColumnsCdkTableApp {
-  undefinedColumns;
+  undefinedColumns: string[];
   dataSource: FakeDataSource = new FakeDataSource();
 }
 
@@ -2146,7 +2149,7 @@ class OuterTableApp {
   columnsToRender =
       ['content_column_a', 'content_column_b', 'injected_column_a', 'injected_column_b'];
 
-  firstRow = i => i === 0;
+  firstRow = (i: number) => i === 0;
 }
 
 @Component({
diff --git a/src/cdk/text-field/autofill.spec.ts b/src/cdk/text-field/autofill.spec.ts
index 5f686f4705f4..788b3282bdeb 100644
--- a/src/cdk/text-field/autofill.spec.ts
+++ b/src/cdk/text-field/autofill.spec.ts
@@ -99,7 +99,7 @@ describe('AutofillMonitor', () => {
     const inputEl = testComponent.input1.nativeElement;
     let animationStartCallback: Function = () => {};
     let autofillStreamEvent: AutofillEvent | null = null;
-    inputEl.addEventListener.and.callFake((_, cb) => animationStartCallback = cb);
+    inputEl.addEventListener.and.callFake((_: string, cb: Function) => animationStartCallback = cb);
     const autofillStream = autofillMonitor.monitor(inputEl);
     autofillStream.subscribe(event => autofillStreamEvent = event);
     expect(autofillStreamEvent).toBeNull();
@@ -114,7 +114,7 @@ describe('AutofillMonitor', () => {
     const inputEl = testComponent.input1.nativeElement;
     let animationStartCallback: Function = () => {};
     let autofillStreamEvent: AutofillEvent | null = null;
-    inputEl.addEventListener.and.callFake((_, cb) => animationStartCallback = cb);
+    inputEl.addEventListener.and.callFake((_: string, cb: Function) => animationStartCallback = cb);
     const autofillStream = autofillMonitor.monitor(inputEl);
     autofillStream.subscribe(event => autofillStreamEvent = event);
     animationStartCallback({animationName: 'cdk-text-field-autofill-start', target: inputEl});
@@ -129,7 +129,7 @@ describe('AutofillMonitor', () => {
   it('should cleanup filled class if monitoring stopped in autofilled state', () => {
     const inputEl = testComponent.input1.nativeElement;
     let animationStartCallback: Function = () => {};
-    inputEl.addEventListener.and.callFake((_, cb) => animationStartCallback = cb);
+    inputEl.addEventListener.and.callFake((_: string, cb: Function) => animationStartCallback = cb);
     autofillMonitor.monitor(inputEl);
     animationStartCallback({animationName: 'cdk-text-field-autofill-start', target: inputEl});
     expect(inputEl.classList).toContain('cdk-text-field-autofilled');
@@ -153,7 +153,7 @@ describe('AutofillMonitor', () => {
   it('should emit on stream inside the NgZone', () => {
     const inputEl = testComponent.input1.nativeElement;
     let animationStartCallback: Function = () => {};
-    inputEl.addEventListener.and.callFake((_, cb) => animationStartCallback = cb);
+    inputEl.addEventListener.and.callFake((_: string, cb: Function) => animationStartCallback = cb);
     const autofillStream = autofillMonitor.monitor(inputEl);
     const spy = jasmine.createSpy('autofill spy');
 
@@ -167,7 +167,7 @@ describe('AutofillMonitor', () => {
   it('should not emit on init if input is unfilled', () => {
     const inputEl = testComponent.input1.nativeElement;
     let animationStartCallback: Function = () => {};
-    inputEl.addEventListener.and.callFake((_, cb) => animationStartCallback = cb);
+    inputEl.addEventListener.and.callFake((_: string, cb: Function) => animationStartCallback = cb);
     const autofillStream = autofillMonitor.monitor(inputEl);
     const spy = jasmine.createSpy('autofill spy');
     autofillStream.subscribe(() => spy());
diff --git a/src/cdk/text-field/autofill.ts b/src/cdk/text-field/autofill.ts
index ee4d2c1ad796..bf85958c86e6 100644
--- a/src/cdk/text-field/autofill.ts
+++ b/src/cdk/text-field/autofill.ts
@@ -113,15 +113,15 @@ export class AutofillMonitor implements OnDestroy {
    * Stop monitoring the autofill state of the given input element.
    * @param element The element to stop monitoring.
    */
-  stopMonitoring(element: Element);
+  stopMonitoring(element: Element): void;
 
   /**
    * Stop monitoring the autofill state of the given input element.
    * @param element The element to stop monitoring.
    */
-  stopMonitoring(element: ElementRef<Element>);
+  stopMonitoring(element: ElementRef<Element>): void;
 
-  stopMonitoring(elementOrRef: Element | ElementRef<Element>) {
+  stopMonitoring(elementOrRef: Element | ElementRef<Element>): void {
     const element = elementOrRef instanceof ElementRef ? elementOrRef.nativeElement : elementOrRef;
     const info = this._monitoredElements.get(element);
 
diff --git a/src/cdk/text-field/autosize.ts b/src/cdk/text-field/autosize.ts
index 2df4384b9e13..d7b60aee7d9a 100644
--- a/src/cdk/text-field/autosize.ts
+++ b/src/cdk/text-field/autosize.ts
@@ -90,7 +90,7 @@ export class CdkTextareaAutosize implements AfterViewInit, DoCheck, OnDestroy {
         `${this.minRows * this._cachedLineHeight}px` : null;
 
     if (minHeight)  {
-      this._setTextareaStyle('minHeight', minHeight);
+      this._textareaElement.style.minHeight = minHeight;
     }
   }
 
@@ -100,7 +100,7 @@ export class CdkTextareaAutosize implements AfterViewInit, DoCheck, OnDestroy {
         `${this.maxRows * this._cachedLineHeight}px` : null;
 
     if (maxHeight) {
-      this._setTextareaStyle('maxHeight', maxHeight);
+      this._textareaElement.style.maxHeight = maxHeight;
     }
   }
 
@@ -124,11 +124,6 @@ export class CdkTextareaAutosize implements AfterViewInit, DoCheck, OnDestroy {
     this._destroyed.complete();
   }
 
-  /** Sets a style property on the textarea element. */
-  private _setTextareaStyle(property: string, value: string): void {
-    this._textareaElement.style[property] = value;
-  }
-
   /**
    * Cache the height of a single-row textarea if it has not already been cached.
    *
diff --git a/src/cdk/tree/control/flat-tree-control.spec.ts b/src/cdk/tree/control/flat-tree-control.spec.ts
index 66736a124e8d..349043d80600 100644
--- a/src/cdk/tree/control/flat-tree-control.spec.ts
+++ b/src/cdk/tree/control/flat-tree-control.spec.ts
@@ -93,8 +93,7 @@ describe('CdkFlatTreeControl', () => {
       const numChildren = 4;
       const numGrandChildren = 2;
       const nodes = generateData(numNodes, numChildren, numGrandChildren);
-
-      let data = [];
+      const data: TestData[] = [];
       flatten(nodes, data);
       treeControl.dataNodes = data;
 
@@ -122,7 +121,7 @@ describe('CdkFlatTreeControl', () => {
       const numChildren = 4;
       const numGrandChildren = 2;
       const nodes = generateData(numNodes, numChildren, numGrandChildren);
-      let data = [];
+      const data: TestData[] = [];
       flatten(nodes, data);
       treeControl.dataNodes = data;
 
diff --git a/src/cdk/tree/control/nested-tree-control.ts b/src/cdk/tree/control/nested-tree-control.ts
index 94692cdd6dfe..82e0c484c7aa 100644
--- a/src/cdk/tree/control/nested-tree-control.ts
+++ b/src/cdk/tree/control/nested-tree-control.ts
@@ -32,7 +32,8 @@ export class NestedTreeControl<T> extends BaseTreeControl<T> {
 
   /** Gets a list of descendant dataNodes of a subtree rooted at given data node recursively. */
   getDescendants(dataNode: T): T[] {
-    const descendants = [];
+    const descendants: T[] = [];
+
     this._getDescendants(descendants, dataNode);
     // Remove the node itself
     return descendants.splice(1);
diff --git a/src/cdk/tree/tree.spec.ts b/src/cdk/tree/tree.spec.ts
index a0bc36891661..24e40195ec6c 100644
--- a/src/cdk/tree/tree.spec.ts
+++ b/src/cdk/tree/tree.spec.ts
@@ -6,7 +6,7 @@
  * found in the LICENSE file at https://angular.io/license
  */
 import {ComponentFixture, TestBed, fakeAsync, flush} from '@angular/core/testing';
-import {Component, ViewChild, TrackByFunction} from '@angular/core';
+import {Component, ViewChild, TrackByFunction, Type} from '@angular/core';
 
 import {CollectionViewer, DataSource} from '@angular/cdk/collections';
 import {combineLatest, BehaviorSubject, Observable} from 'rxjs';
@@ -28,7 +28,7 @@ describe('CdkTree', () => {
   let treeElement: HTMLElement;
   let tree: CdkTree<TestData>;
 
-  function configureCdkTreeTestingModule(declarations) {
+  function configureCdkTreeTestingModule(declarations: Type<any>[]) {
     TestBed.configureTestingModule({
       imports: [CdkTreeModule],
       declarations: declarations,
diff --git a/src/cdk/tsconfig-build.json b/src/cdk/tsconfig-build.json
index 225a71beced1..0a90a76732ea 100644
--- a/src/cdk/tsconfig-build.json
+++ b/src/cdk/tsconfig-build.json
@@ -8,6 +8,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "importHelpers": true,
     "newLine": "lf",
     "module": "es2015",
diff --git a/src/demo-app/tsconfig-aot.json b/src/demo-app/tsconfig-aot.json
index 8ecd826b8a57..1a78a695cd8b 100644
--- a/src/demo-app/tsconfig-aot.json
+++ b/src/demo-app/tsconfig-aot.json
@@ -9,6 +9,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "outDir": "../../dist/packages/demo-app",
     "rootDirs": [
       ".",
diff --git a/src/lib/autocomplete/autocomplete-trigger.ts b/src/lib/autocomplete/autocomplete-trigger.ts
index b1ae2efd0c00..0e9f3bcfa2f4 100644
--- a/src/lib/autocomplete/autocomplete-trigger.ts
+++ b/src/lib/autocomplete/autocomplete-trigger.ts
@@ -120,6 +120,7 @@ export class MatAutocompleteTrigger implements ControlValueAccessor, OnDestroy {
   private _portal: TemplatePortal;
   private _componentDestroyed = false;
   private _autocompleteDisabled = false;
+  private _scrollStrategy: () => ScrollStrategy;
 
   /** Old value of the native input. Used to work around issues with the `input` event on IE. */
   private _previousValue: string | number | null;
@@ -193,7 +194,7 @@ export class MatAutocompleteTrigger implements ControlValueAccessor, OnDestroy {
               private _viewContainerRef: ViewContainerRef,
               private _zone: NgZone,
               private _changeDetectorRef: ChangeDetectorRef,
-              @Inject(MAT_AUTOCOMPLETE_SCROLL_STRATEGY) private _scrollStrategy,
+              @Inject(MAT_AUTOCOMPLETE_SCROLL_STRATEGY) scrollStrategy: any,
               @Optional() private _dir: Directionality,
               @Optional() @Host() private _formField: MatFormField,
               @Optional() @Inject(DOCUMENT) private _document: any,
@@ -205,6 +206,8 @@ export class MatAutocompleteTrigger implements ControlValueAccessor, OnDestroy {
         window.addEventListener('blur', this._windowBlurHandler);
       });
     }
+
+    this._scrollStrategy = scrollStrategy;
   }
 
   ngOnDestroy() {
diff --git a/src/lib/checkbox/checkbox.spec.ts b/src/lib/checkbox/checkbox.spec.ts
index 855b7f1d1015..f5838aaf7144 100644
--- a/src/lib/checkbox/checkbox.spec.ts
+++ b/src/lib/checkbox/checkbox.spec.ts
@@ -1206,7 +1206,7 @@ class CheckboxWithTabIndex {
     <mat-checkbox></mat-checkbox>`,
 })
 class CheckboxUsingViewChild {
-  @ViewChild(MatCheckbox) checkbox;
+  @ViewChild(MatCheckbox) checkbox: MatCheckbox;
 
   set isDisabled(value: boolean) {
     this.checkbox.disabled = value;
diff --git a/src/lib/core/common-behaviors/common-module.ts b/src/lib/core/common-behaviors/common-module.ts
index 42081f87c05a..6162e8df3da2 100644
--- a/src/lib/core/common-behaviors/common-module.ts
+++ b/src/lib/core/common-behaviors/common-module.ts
@@ -63,7 +63,8 @@ export class MatCommonModule {
 
   /** Whether the code is running in tests. */
   private _isTestEnv() {
-    return this._window && (this._window['__karma__'] || this._window['jasmine']);
+    const window = this._window as any;
+    return window && (window.__karma__ || window.jasmine);
   }
 
   private _checkDoctypeIsDefined(): void {
@@ -109,7 +110,7 @@ export class MatCommonModule {
       return;
     }
 
-    if (this._areChecksEnabled() && !this._window['Hammer'] && !this._hammerLoader) {
+    if (this._areChecksEnabled() && !(this._window as any)['Hammer'] && !this._hammerLoader) {
       console.warn(
         'Could not find HammerJS. Certain Angular Material components may not work correctly.');
     }
diff --git a/src/lib/core/common-behaviors/error-state.ts b/src/lib/core/common-behaviors/error-state.ts
index a5514fb6105e..819028e48d76 100644
--- a/src/lib/core/common-behaviors/error-state.ts
+++ b/src/lib/core/common-behaviors/error-state.ts
@@ -14,7 +14,7 @@ import {Constructor} from './constructor';
 
 /** @docs-private */
 export interface CanUpdateErrorState {
-  updateErrorState();
+  updateErrorState(): void;
   readonly stateChanges: Subject<void>;
   errorState: boolean;
   errorStateMatcher: ErrorStateMatcher;
diff --git a/src/lib/core/gestures/gesture-config.spec.ts b/src/lib/core/gestures/gesture-config.spec.ts
index 020e1fb1371c..8bc8f060b1de 100644
--- a/src/lib/core/gestures/gesture-config.spec.ts
+++ b/src/lib/core/gestures/gesture-config.spec.ts
@@ -17,7 +17,7 @@ describe('GestureConfig', () => {
     const fixture = TestBed.createComponent(ButtonWithLongpressHander);
     fixture.detectChanges();
 
-    expect(window['Hammer']).toHaveBeenCalled();
+    expect((window as any).Hammer).toHaveBeenCalled();
   });
 
   it('should be able to pass options to HammerJS', () => {
@@ -38,7 +38,7 @@ describe('GestureConfig', () => {
     fixture.detectChanges();
 
     const button = fixture.debugElement.nativeElement.querySelector('button');
-    const firstCallArgs = window['Hammer'].calls.first().args;
+    const firstCallArgs = (window as any).Hammer.calls.first().args;
 
     expect(firstCallArgs[0]).toBe(button);
     expect(firstCallArgs[1].cssProps.touchAction).toBe('auto');
diff --git a/src/lib/core/ripple/ripple.spec.ts b/src/lib/core/ripple/ripple.spec.ts
index a0e72ec1992b..9fd99c2c9546 100644
--- a/src/lib/core/ripple/ripple.spec.ts
+++ b/src/lib/core/ripple/ripple.spec.ts
@@ -24,7 +24,7 @@ describe('MatRipple', () => {
   let platform: Platform;
 
   /** Extracts the numeric value of a pixel size string like '123px'. */
-  const pxStringToFloat = s => parseFloat(s) || 0;
+  const pxStringToFloat = (s: string | null) => s ? parseFloat(s) : 0;
   const startingWindowWidth = window.innerWidth;
   const startingWindowHeight = window.innerHeight;
 
diff --git a/src/lib/datepicker/datepicker.ts b/src/lib/datepicker/datepicker.ts
index 784c01bb2cd6..88973e51e235 100644
--- a/src/lib/datepicker/datepicker.ts
+++ b/src/lib/datepicker/datepicker.ts
@@ -139,6 +139,8 @@ export class MatDatepickerContent<D> extends _MatDatepickerContentMixinBase
   encapsulation: ViewEncapsulation.None,
 })
 export class MatDatepicker<D> implements OnDestroy, CanColor {
+  private _scrollStrategy: () => ScrollStrategy;
+
   /** An input indicating the type of the custom header component for the calendar, if set. */
   @Input() calendarHeaderComponent: ComponentType<any>;
 
@@ -276,13 +278,15 @@ export class MatDatepicker<D> implements OnDestroy, CanColor {
               private _overlay: Overlay,
               private _ngZone: NgZone,
               private _viewContainerRef: ViewContainerRef,
-              @Inject(MAT_DATEPICKER_SCROLL_STRATEGY) private _scrollStrategy,
+              @Inject(MAT_DATEPICKER_SCROLL_STRATEGY) scrollStrategy: any,
               @Optional() private _dateAdapter: DateAdapter<D>,
               @Optional() private _dir: Directionality,
               @Optional() @Inject(DOCUMENT) private _document: any) {
     if (!this._dateAdapter) {
       throw createMissingDateImplError('DateAdapter');
     }
+
+    this._scrollStrategy = scrollStrategy;
   }
 
   ngOnDestroy() {
diff --git a/src/lib/dialog/dialog.ts b/src/lib/dialog/dialog.ts
index 61942d5a9651..e1be22a997ef 100644
--- a/src/lib/dialog/dialog.ts
+++ b/src/lib/dialog/dialog.ts
@@ -45,13 +45,13 @@ export const MAT_DIALOG_SCROLL_STRATEGY =
     new InjectionToken<() => ScrollStrategy>('mat-dialog-scroll-strategy');
 
 /** @docs-private */
-export function MAT_DIALOG_SCROLL_STRATEGY_FACTORY(overlay: Overlay): ()  => ScrollStrategy {
+export function MAT_DIALOG_SCROLL_STRATEGY_FACTORY(overlay: Overlay): () => ScrollStrategy {
   return () => overlay.scrollStrategies.block();
 }
 
 /** @docs-private */
 export function MAT_DIALOG_SCROLL_STRATEGY_PROVIDER_FACTORY(overlay: Overlay):
-    () => ScrollStrategy {
+  () => ScrollStrategy {
   return () => overlay.scrollStrategies.block();
 }
 
@@ -72,6 +72,7 @@ export class MatDialog implements OnDestroy {
   private readonly _afterAllClosedAtThisLevel = new Subject<void>();
   private readonly _afterOpenedAtThisLevel = new Subject<MatDialogRef<any>>();
   private _ariaHiddenElements = new Map<Element, string|null>();
+  private _scrollStrategy: () => ScrollStrategy;
 
   /** Keeps track of the currently-open dialogs. */
   get openDialogs(): MatDialogRef<any>[] {
@@ -92,7 +93,7 @@ export class MatDialog implements OnDestroy {
     return this.afterOpened;
   }
 
-  get _afterAllClosed() {
+  get _afterAllClosed(): Subject<void> {
     const parent = this._parentDialog;
     return parent ? parent._afterAllClosed : this._afterAllClosedAtThisLevel;
   }
@@ -109,10 +110,12 @@ export class MatDialog implements OnDestroy {
       private _overlay: Overlay,
       private _injector: Injector,
       @Optional() private _location: Location,
-      @Optional() @Inject(MAT_DIALOG_DEFAULT_OPTIONS) private _defaultOptions,
-      @Inject(MAT_DIALOG_SCROLL_STRATEGY) private _scrollStrategy,
+      @Optional() @Inject(MAT_DIALOG_DEFAULT_OPTIONS) private _defaultOptions: MatDialogConfig,
+      @Inject(MAT_DIALOG_SCROLL_STRATEGY) scrollStrategy: any,
       @Optional() @SkipSelf() private _parentDialog: MatDialog,
-      private _overlayContainer: OverlayContainer) {}
+      private _overlayContainer: OverlayContainer) {
+    this._scrollStrategy = scrollStrategy;
+  }
 
   /**
    * Opens a modal dialog containing the given component.
diff --git a/src/lib/form-field/form-field.ts b/src/lib/form-field/form-field.ts
index f5278c035a4b..0da9926aa78a 100644
--- a/src/lib/form-field/form-field.ts
+++ b/src/lib/form-field/form-field.ts
@@ -50,6 +50,7 @@ import {MatPlaceholder} from './placeholder';
 import {MatPrefix} from './prefix';
 import {MatSuffix} from './suffix';
 import {Platform} from '@angular/cdk/platform';
+import {NgControl} from '@angular/forms';
 import {ANIMATION_MODULE_TYPE} from '@angular/platform-browser/animations';
 
 
@@ -317,7 +318,7 @@ export class MatFormField extends _MatFormFieldMixinBase
   }
 
   /** Determines whether a class from the NgControl should be forwarded to the host element. */
-  _shouldForward(prop: string): boolean {
+  _shouldForward(prop: keyof NgControl): boolean {
     const ngControl = this._control ? this._control.ngControl : null;
     return ngControl && ngControl[prop];
   }
diff --git a/src/lib/grid-list/grid-list.ts b/src/lib/grid-list/grid-list.ts
index 0a15d12ad01e..2abb94d617cc 100644
--- a/src/lib/grid-list/grid-list.ts
+++ b/src/lib/grid-list/grid-list.ts
@@ -166,7 +166,7 @@ export class MatGridList implements MatGridListBase, OnInit, AfterContentChecked
   /** Sets style on the main grid-list element, given the style name and value. */
   _setListStyle(style: [string, string | null] | null): void {
     if (style) {
-      this._element.nativeElement.style[style[0]] = style[1];
+      (this._element.nativeElement.style as any)[style[0]] = style[1];
     }
   }
 }
diff --git a/src/lib/grid-list/grid-tile.ts b/src/lib/grid-list/grid-tile.ts
index 1e3817a983e2..c6251fb2a9d6 100644
--- a/src/lib/grid-list/grid-tile.ts
+++ b/src/lib/grid-list/grid-tile.ts
@@ -58,7 +58,7 @@ export class MatGridTile {
    * "Changed after checked" errors that would occur with HostBinding.
    */
   _setStyle(property: string, value: any): void {
-    this._element.nativeElement.style[property] = value;
+    (this._element.nativeElement.style as any)[property] = value;
   }
 }
 
diff --git a/src/lib/grid-list/tile-styler.ts b/src/lib/grid-list/tile-styler.ts
index 4d6ed2b978ca..3838e84978c7 100644
--- a/src/lib/grid-list/tile-styler.ts
+++ b/src/lib/grid-list/tile-styler.ts
@@ -138,7 +138,7 @@ export abstract class TileStyler {
    * @docs-private
    */
   abstract setRowStyles(tile: MatGridTile, rowIndex: number, percentWidth: number,
-                        gutterWidth: number);
+                        gutterWidth: number): void;
 
   /**
    * Calculates the computed height and returns the correct style property to set.
@@ -152,7 +152,7 @@ export abstract class TileStyler {
    * @param list Grid list that the styler was attached to.
    * @docs-private
    */
-  abstract reset(list: MatGridList);
+  abstract reset(list: MatGridList): void;
 }
 
 
diff --git a/src/lib/list/selection-list.spec.ts b/src/lib/list/selection-list.spec.ts
index 7657dedc10b5..8f3abdd5679a 100644
--- a/src/lib/list/selection-list.spec.ts
+++ b/src/lib/list/selection-list.spec.ts
@@ -975,7 +975,7 @@ describe('MatSelectionList with forms', () => {
       const fixture = TestBed.createComponent(SelectionListWithCustomComparator);
       const testComponent = fixture.componentInstance;
 
-      testComponent.compareWith = jasmine.createSpy('comparator', (o1, o2) => {
+      testComponent.compareWith = jasmine.createSpy('comparator', (o1: any, o2: any) => {
         return o1 && o2 && o1.id === o2.id;
       }).and.callThrough();
 
diff --git a/src/lib/menu/menu-trigger.ts b/src/lib/menu/menu-trigger.ts
index 88b5112d919b..0f6ddb9749de 100644
--- a/src/lib/menu/menu-trigger.ts
+++ b/src/lib/menu/menu-trigger.ts
@@ -15,8 +15,8 @@ import {
   Overlay,
   OverlayConfig,
   OverlayRef,
-  ScrollStrategy,
   VerticalConnectionPos,
+  ScrollStrategy,
 } from '@angular/cdk/overlay';
 import {TemplatePortal} from '@angular/cdk/portal';
 import {
@@ -83,6 +83,7 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
   private _menuOpen: boolean = false;
   private _closeSubscription = Subscription.EMPTY;
   private _hoverSubscription = Subscription.EMPTY;
+  private _scrollStrategy: () => ScrollStrategy;
 
   // Tracking input type is necessary so it's possible to only auto-focus
   // the first item of the list when the menu is opened via the keyboard
@@ -132,7 +133,7 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
   constructor(private _overlay: Overlay,
               private _element: ElementRef<HTMLElement>,
               private _viewContainerRef: ViewContainerRef,
-              @Inject(MAT_MENU_SCROLL_STRATEGY) private _scrollStrategy,
+              @Inject(MAT_MENU_SCROLL_STRATEGY) scrollStrategy: any,
               @Optional() private _parentMenu: MatMenu,
               @Optional() @Self() private _menuItemInstance: MatMenuItem,
               @Optional() private _dir: Directionality,
@@ -143,12 +144,14 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
     if (_menuItemInstance) {
       _menuItemInstance._triggersSubmenu = this.triggersSubmenu();
     }
+
+    this._scrollStrategy = scrollStrategy;
   }
 
   ngAfterContentInit() {
     this._checkMenu();
 
-    this.menu.close.subscribe(reason => {
+    this.menu.close.asObservable().subscribe(reason => {
       this._destroyMenu();
 
       // If a click closed the menu, we should close the entire chain of nested menus.
diff --git a/src/lib/menu/menu.spec.ts b/src/lib/menu/menu.spec.ts
index 70eb2e4131aa..834e7b56fea5 100644
--- a/src/lib/menu/menu.spec.ts
+++ b/src/lib/menu/menu.spec.ts
@@ -800,7 +800,8 @@ describe('MatMenu', () => {
 
       constructor(ctor: {new(): T; }, inputs: {[key: string]: any} = {}) {
         this.fixture = createComponent(ctor);
-        Object.keys(inputs).forEach(key => this.fixture.componentInstance[key] = inputs[key]);
+        Object.keys(inputs)
+            .forEach(key => (this.fixture.componentInstance as any)[key] = inputs[key]);
         this.fixture.detectChanges();
         this.trigger = this.fixture.componentInstance.triggerEl.nativeElement;
       }
diff --git a/src/lib/radio/radio.spec.ts b/src/lib/radio/radio.spec.ts
index 60c5c50042d0..68692baf4ee9 100644
--- a/src/lib/radio/radio.spec.ts
+++ b/src/lib/radio/radio.spec.ts
@@ -835,7 +835,7 @@ class RadioGroupWithNgModel {
   template: `<mat-radio-button>One</mat-radio-button>`
 })
 class DisableableRadioButton {
-  @ViewChild(MatRadioButton) matRadioButton;
+  @ViewChild(MatRadioButton) matRadioButton: MatRadioButton;
 
   set disabled(value: boolean) {
     this.matRadioButton.disabled = value;
diff --git a/src/lib/select/select.spec.ts b/src/lib/select/select.spec.ts
index 1057158e8cb2..5e6d2d5d5080 100644
--- a/src/lib/select/select.spec.ts
+++ b/src/lib/select/select.spec.ts
@@ -2926,7 +2926,7 @@ describe('MatSelect', () => {
       const overlayTop = overlayPane.getBoundingClientRect().top;
       const options = overlayPane.querySelectorAll('mat-option');
       const optionTop = options[index].getBoundingClientRect().top;
-      const triggerFontSize = parseInt(window.getComputedStyle(trigger)['font-size']);
+      const triggerFontSize = parseInt(window.getComputedStyle(trigger).fontSize || '0');
       const triggerLineHeightEm = 1.125;
 
       // Extra trigger height beyond the font size caused by the fact that the line-height is
diff --git a/src/lib/select/select.ts b/src/lib/select/select.ts
index 8cedce985230..7a3bbd02d0f5 100644
--- a/src/lib/select/select.ts
+++ b/src/lib/select/select.ts
@@ -21,12 +21,7 @@ import {
   SPACE,
   UP_ARROW,
 } from '@angular/cdk/keycodes';
-import {
-  CdkConnectedOverlay,
-  Overlay,
-  RepositionScrollStrategy,
-  ScrollStrategy,
-} from '@angular/cdk/overlay';
+import {CdkConnectedOverlay, Overlay, ScrollStrategy} from '@angular/cdk/overlay';
 import {ViewportRuler} from '@angular/cdk/scrolling';
 import {
   AfterContentInit,
@@ -141,7 +136,7 @@ export const MAT_SELECT_SCROLL_STRATEGY =
 
 /** @docs-private */
 export function MAT_SELECT_SCROLL_STRATEGY_PROVIDER_FACTORY(overlay: Overlay):
-    () => RepositionScrollStrategy {
+    () => ScrollStrategy {
   return () => overlay.scrollStrategies.reposition();
 }
 
@@ -230,6 +225,8 @@ export class MatSelectTrigger {}
 export class MatSelect extends _MatSelectMixinBase implements AfterContentInit, OnChanges,
     OnDestroy, OnInit, DoCheck, ControlValueAccessor, CanDisable, HasTabIndex,
     MatFormFieldControl<any>, CanUpdateErrorState, CanDisableRipple {
+  private _scrollStrategyFactory: () => ScrollStrategy;
+
   /** Whether or not the overlay panel is open. */
   private _panelOpen = false;
 
@@ -285,7 +282,7 @@ export class MatSelect extends _MatSelectMixinBase implements AfterContentInit,
   _panelDoneAnimatingStream = new Subject<string>();
 
   /** Strategy that will be used to handle scrolling while the select panel is open. */
-  _scrollStrategy = this._scrollStrategyFactory();
+  _scrollStrategy: ScrollStrategy;
 
   /**
    * The y-offset of the overlay panel in relation to the trigger's top start corner.
@@ -487,7 +484,7 @@ export class MatSelect extends _MatSelectMixinBase implements AfterContentInit,
     @Optional() private _parentFormField: MatFormField,
     @Self() @Optional() public ngControl: NgControl,
     @Attribute('tabindex') tabIndex: string,
-    @Inject(MAT_SELECT_SCROLL_STRATEGY) private _scrollStrategyFactory) {
+    @Inject(MAT_SELECT_SCROLL_STRATEGY) scrollStrategyFactory: any) {
     super(elementRef, _defaultErrorStateMatcher, _parentForm,
           _parentFormGroup, ngControl);
 
@@ -497,6 +494,8 @@ export class MatSelect extends _MatSelectMixinBase implements AfterContentInit,
       this.ngControl.valueAccessor = this;
     }
 
+    this._scrollStrategyFactory = scrollStrategyFactory;
+    this._scrollStrategy = this._scrollStrategyFactory();
     this.tabIndex = parseInt(tabIndex) || 0;
 
     // Force setter to be called in case id was not specified.
@@ -572,7 +571,7 @@ export class MatSelect extends _MatSelectMixinBase implements AfterContentInit,
     this._triggerRect = this.trigger.nativeElement.getBoundingClientRect();
     // Note: The computed font-size will be a string pixel value (e.g. "16px").
     // `parseInt` ignores the trailing 'px' and converts this to a number.
-    this._triggerFontSize = parseInt(getComputedStyle(this.trigger.nativeElement)['font-size']);
+    this._triggerFontSize = parseInt(getComputedStyle(this.trigger.nativeElement).fontSize || '0');
 
     this._panelOpen = true;
     this._keyManager.withHorizontalOrientation(null);
diff --git a/src/lib/sidenav/drawer.spec.ts b/src/lib/sidenav/drawer.spec.ts
index 5f05140dd47a..c8b57197475f 100644
--- a/src/lib/sidenav/drawer.spec.ts
+++ b/src/lib/sidenav/drawer.spec.ts
@@ -99,9 +99,10 @@ describe('MatDrawer', () => {
     it('should resolve the open method promise with the new state of the drawer', fakeAsync(() => {
       const fixture = TestBed.createComponent(BasicTestApp);
       fixture.detectChanges();
-      const drawer = fixture.debugElement.query(By.directive(MatDrawer));
+      const drawer: MatDrawer =
+          fixture.debugElement.query(By.directive(MatDrawer)).componentInstance;
 
-      drawer.componentInstance.open().then(result => expect(result).toBe('open'));
+      drawer.open().then(result => expect(result).toBe('open'));
       fixture.detectChanges();
       tick();
       fixture.detectChanges();
@@ -111,13 +112,14 @@ describe('MatDrawer', () => {
       const fixture = TestBed.createComponent(BasicTestApp);
       fixture.detectChanges();
       const drawer = fixture.debugElement.query(By.directive(MatDrawer));
+      const drawerInstance: MatDrawer = drawer.componentInstance;
 
-      drawer.componentInstance.open();
+      drawerInstance.open();
       fixture.detectChanges();
       flush();
       fixture.detectChanges();
 
-      drawer.componentInstance.close().then(result => expect(result).toBe('close'));
+      drawerInstance.close().then(result => expect(result).toBe('close'));
       fixture.detectChanges();
       flush();
       fixture.detectChanges();
diff --git a/src/lib/stepper/stepper.spec.ts b/src/lib/stepper/stepper.spec.ts
index d7fae0567f00..de5d8f033fc6 100644
--- a/src/lib/stepper/stepper.spec.ts
+++ b/src/lib/stepper/stepper.spec.ts
@@ -369,7 +369,7 @@ describe('MatStepper', () => {
   });
 
   describe('basic stepper with i18n label change', () => {
-    let i18nFixture;
+    let i18nFixture: ComponentFixture<SimpleMatHorizontalStepperApp>;
 
     beforeEach(() => {
       i18nFixture = createComponent(SimpleMatHorizontalStepperApp);
@@ -688,7 +688,7 @@ describe('MatStepper', () => {
   });
 
   describe('linear stepper with a pre-defined selectedIndex', () => {
-    let preselectedFixture;
+    let preselectedFixture: ComponentFixture<SimplePreselectedMatHorizontalStepperApp>;
     beforeEach(() => {
       preselectedFixture = createComponent(SimplePreselectedMatHorizontalStepperApp);
     });
@@ -699,7 +699,7 @@ describe('MatStepper', () => {
   });
 
   describe('linear stepper with no `stepControl`', () => {
-    let noStepControlFixture;
+    let noStepControlFixture: ComponentFixture<SimpleStepperWithoutStepControl>;
     beforeEach(() => {
       noStepControlFixture = createComponent(SimpleStepperWithoutStepControl);
       noStepControlFixture.detectChanges();
@@ -721,7 +721,7 @@ describe('MatStepper', () => {
   });
 
   describe('linear stepper with `stepControl`', () => {
-    let controlAndBindingFixture;
+    let controlAndBindingFixture: ComponentFixture<SimpleStepperWithStepControlAndCompletedBinding>;
     beforeEach(() => {
       controlAndBindingFixture =
       createComponent(SimpleStepperWithStepControlAndCompletedBinding);
@@ -1326,7 +1326,7 @@ class SimpleStepperWithStepControlAndCompletedBinding {
 })
 class IconOverridesStepper {
   getRomanNumeral(value: number) {
-    return {
+    const numberMap: {[key: number]: string} = {
       1: 'I',
       2: 'II',
       3: 'III',
@@ -1336,7 +1336,9 @@ class IconOverridesStepper {
       7: 'VII',
       8: 'VIII',
       9: 'IX'
-    }[value];
+    };
+
+    return numberMap[value];
   }
 }
 
diff --git a/src/lib/table/table-data-source.ts b/src/lib/table/table-data-source.ts
index ad7e5c14cf6a..d04f7248603e 100644
--- a/src/lib/table/table-data-source.ts
+++ b/src/lib/table/table-data-source.ts
@@ -108,7 +108,7 @@ export class MatTableDataSource<T> extends DataSource<T> {
    */
   sortingDataAccessor: ((data: T, sortHeaderId: string) => string|number) =
       (data: T, sortHeaderId: string): string|number => {
-    const value: any = data[sortHeaderId];
+    const value = (data as {[key: string]: any})[sortHeaderId];
 
     if (_isNumberValue(value)) {
       const numberValue = Number(value);
@@ -173,7 +173,8 @@ export class MatTableDataSource<T> extends DataSource<T> {
    */
   filterPredicate: ((data: T, filter: string) => boolean) = (data: T, filter: string): boolean => {
     // Transform the data into a lowercase string of all property values.
-    const accumulator = (currentTerm, key) => currentTerm + data[key];
+    const accumulator =
+        (currentTerm: string, key: string) => currentTerm + (data as {[key: string]: any})[key];
     const dataStr = Object.keys(data).reduce(accumulator, '').toLowerCase();
 
     // Transform the filter by converting it to lowercase and removing whitespace.
diff --git a/src/lib/tabs/tab-body.ts b/src/lib/tabs/tab-body.ts
index 802925a23aa5..2440d2d3c08c 100644
--- a/src/lib/tabs/tab-body.ts
+++ b/src/lib/tabs/tab-body.ts
@@ -161,7 +161,7 @@ export class MatTabBody implements OnInit, OnDestroy {
               changeDetectorRef?: ChangeDetectorRef) {
 
     if (this._dir && changeDetectorRef) {
-      this._dirChangeSubscription = this._dir.change.subscribe(dir => {
+      this._dirChangeSubscription = this._dir.change.subscribe((dir: Direction) => {
         this._computePositionAnimationState(dir);
         changeDetectorRef.markForCheck();
       });
diff --git a/src/lib/toolbar/toolbar.ts b/src/lib/toolbar/toolbar.ts
index ff998613a91e..1f672d18afd6 100644
--- a/src/lib/toolbar/toolbar.ts
+++ b/src/lib/toolbar/toolbar.ts
@@ -88,10 +88,10 @@ export class MatToolbar extends _MatToolbarMixinBase implements CanColor, AfterV
 
     // Check if there are any other DOM nodes that can display content but aren't inside of
     // a <mat-toolbar-row> element.
-    const isCombinedUsage = [].slice.call(this._elementRef.nativeElement.childNodes)
+    const isCombinedUsage = Array.from<HTMLElement>(this._elementRef.nativeElement.childNodes)
       .filter(node => !(node.classList && node.classList.contains('mat-toolbar-row')))
       .filter(node => node.nodeType !== (this._document ? this._document.COMMENT_NODE : 8))
-      .some(node => node.textContent.trim());
+      .some(node => !!(node.textContent && node.textContent.trim()));
 
     if (isCombinedUsage) {
       throwToolbarMixedModesError();
diff --git a/src/lib/tooltip/tooltip.ts b/src/lib/tooltip/tooltip.ts
index 212c66c283d9..83690831db0f 100644
--- a/src/lib/tooltip/tooltip.ts
+++ b/src/lib/tooltip/tooltip.ts
@@ -18,8 +18,8 @@ import {
   Overlay,
   OverlayConnectionPosition,
   OverlayRef,
-  ScrollStrategy,
   VerticalConnectionPos,
+  ScrollStrategy,
 } from '@angular/cdk/overlay';
 import {ScrollDispatcher} from '@angular/cdk/scrolling';
 import {Platform} from '@angular/cdk/platform';
@@ -122,6 +122,7 @@ export class MatTooltip implements OnDestroy {
   private _position: TooltipPosition = 'below';
   private _disabled: boolean = false;
   private _tooltipClass: string|string[]|Set<string>|{[key: string]: any};
+  private _scrollStrategy: () => ScrollStrategy;
 
   /** Allows the user to define the position of the tooltip relative to the parent element */
   @Input('matTooltipPosition')
@@ -203,12 +204,14 @@ export class MatTooltip implements OnDestroy {
     private _platform: Platform,
     private _ariaDescriber: AriaDescriber,
     private _focusMonitor: FocusMonitor,
-    @Inject(MAT_TOOLTIP_SCROLL_STRATEGY) private _scrollStrategy,
+    @Inject(MAT_TOOLTIP_SCROLL_STRATEGY) scrollStrategy: any,
     @Optional() private _dir: Directionality,
     @Optional() @Inject(MAT_TOOLTIP_DEFAULT_OPTIONS)
       private _defaultOptions: MatTooltipDefaultOptions) {
 
+    this._scrollStrategy = scrollStrategy;
     const element: HTMLElement = _elementRef.nativeElement;
+    const elementStyle = element.style as CSSStyleDeclaration & {webkitUserDrag: string};
 
     // The mouse events shouldn't be bound on mobile devices, because they can prevent the
     // first tap from firing its click event or can cause the tooltip to open for clicks.
@@ -225,14 +228,14 @@ export class MatTooltip implements OnDestroy {
       // problematic on iOS and in Safari, because it will prevent users from typing in inputs.
       // Since `user-select: none` is not needed for the `longpress` event and can cause unexpected
       // behavior for text fields, we always clear the `user-select` to avoid such issues.
-      element.style.webkitUserSelect = element.style.userSelect = element.style.msUserSelect = '';
+      elementStyle.webkitUserSelect = elementStyle.userSelect = elementStyle.msUserSelect = '';
     }
 
     // Hammer applies `-webkit-user-drag: none` on all elements by default,
     // which breaks the native drag&drop. If the consumer explicitly made
     // the element draggable, clear the `-webkit-user-drag`.
-    if (element.draggable && element.style['webkitUserDrag'] === 'none') {
-      element.style['webkitUserDrag'] = '';
+    if (element.draggable && elementStyle.webkitUserDrag === 'none') {
+      elementStyle.webkitUserDrag = '';
     }
 
     _focusMonitor.monitor(_elementRef).pipe(takeUntil(this._destroyed)).subscribe(origin => {
diff --git a/src/lib/tree/tree.spec.ts b/src/lib/tree/tree.spec.ts
index 5e0fbf3efad7..e9c1e541d0c1 100644
--- a/src/lib/tree/tree.spec.ts
+++ b/src/lib/tree/tree.spec.ts
@@ -6,7 +6,7 @@
  * found in the LICENSE file at https://angular.io/license
  */
 import {FlatTreeControl, NestedTreeControl, TreeControl} from '@angular/cdk/tree';
-import {Component, ViewChild} from '@angular/core';
+import {Component, ViewChild, Type} from '@angular/core';
 import {ComponentFixture, TestBed} from '@angular/core/testing';
 import {BehaviorSubject, Observable} from 'rxjs';
 import {
@@ -25,7 +25,7 @@ describe('MatTree', () => {
   let treeElement: HTMLElement;
   let underlyingDataSource: FakeDataSource;
 
-  function configureMatTreeTestingModule(declarations) {
+  function configureMatTreeTestingModule(declarations: Type<any>[]) {
     TestBed.configureTestingModule({
       imports: [MatTreeModule],
       declarations: declarations,
diff --git a/src/lib/tsconfig-build.json b/src/lib/tsconfig-build.json
index 4c8db831249b..650d784545b9 100644
--- a/src/lib/tsconfig-build.json
+++ b/src/lib/tsconfig-build.json
@@ -7,6 +7,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "importHelpers": true,
     "newLine": "lf",
     "module": "es2015",
diff --git a/src/material-examples/cdk-tree-flat/cdk-tree-flat-example.ts b/src/material-examples/cdk-tree-flat/cdk-tree-flat-example.ts
index 9f9487126ff4..2df6c7cb80a5 100644
--- a/src/material-examples/cdk-tree-flat/cdk-tree-flat-example.ts
+++ b/src/material-examples/cdk-tree-flat/cdk-tree-flat-example.ts
@@ -91,7 +91,7 @@ export class FileDatabase {
    * Build the file structure tree. The `value` is the Json object, or a sub-tree of a Json object.
    * The return value is the list of `FileNode`.
    */
-  buildFileTree(obj: object, level: number): FileNode[] {
+  buildFileTree(obj: {[key: string]: any}, level: number): FileNode[] {
     return Object.keys(obj).reduce<FileNode[]>((accumulator, key) => {
       const value = obj[key];
       const node = new FileNode();
diff --git a/src/material-examples/cdk-tree-nested/cdk-tree-nested-example.ts b/src/material-examples/cdk-tree-nested/cdk-tree-nested-example.ts
index 3809879c66cc..d574910c8ea7 100644
--- a/src/material-examples/cdk-tree-nested/cdk-tree-nested-example.ts
+++ b/src/material-examples/cdk-tree-nested/cdk-tree-nested-example.ts
@@ -84,7 +84,7 @@ export class FileDatabase {
    * Build the file structure tree. The `value` is the Json object, or a sub-tree of a Json object.
    * The return value is the list of `FileNode`.
    */
-  buildFileTree(obj: object, level: number): FileNode[] {
+  buildFileTree(obj: {[key: string]: any}, level: number): FileNode[] {
     return Object.keys(obj).reduce<FileNode[]>((accumulator, key) => {
       const value = obj[key];
       const node = new FileNode();
diff --git a/src/material-examples/sort-overview/sort-overview-example.ts b/src/material-examples/sort-overview/sort-overview-example.ts
index 4062c8238f96..b249f03f1e7b 100644
--- a/src/material-examples/sort-overview/sort-overview-example.ts
+++ b/src/material-examples/sort-overview/sort-overview-example.ts
@@ -53,6 +53,6 @@ export class SortOverviewExample {
   }
 }
 
-function compare(a, b, isAsc) {
+function compare(a: number | string, b: number | string, isAsc: boolean) {
   return (a < b ? -1 : 1) * (isAsc ? 1 : -1);
 }
diff --git a/src/material-examples/tree-checklist/tree-checklist-example.ts b/src/material-examples/tree-checklist/tree-checklist-example.ts
index 2f0318698d56..8d91541e9add 100644
--- a/src/material-examples/tree-checklist/tree-checklist-example.ts
+++ b/src/material-examples/tree-checklist/tree-checklist-example.ts
@@ -68,7 +68,7 @@ export class ChecklistDatabase {
    * Build the file structure tree. The `value` is the Json object, or a sub-tree of a Json object.
    * The return value is the list of `TodoItemNode`.
    */
-  buildFileTree(obj: object, level: number): TodoItemNode[] {
+  buildFileTree(obj: {[key: string]: any}, level: number): TodoItemNode[] {
     return Object.keys(obj).reduce<TodoItemNode[]>((accumulator, key) => {
       const value = obj[key];
       const node = new TodoItemNode();
diff --git a/src/material-examples/tree-flat-overview/tree-flat-overview-example.ts b/src/material-examples/tree-flat-overview/tree-flat-overview-example.ts
index ba7a4dad1d6a..0e5155d104f3 100644
--- a/src/material-examples/tree-flat-overview/tree-flat-overview-example.ts
+++ b/src/material-examples/tree-flat-overview/tree-flat-overview-example.ts
@@ -91,7 +91,7 @@ export class FileDatabase {
    * Build the file structure tree. The `value` is the Json object, or a sub-tree of a Json object.
    * The return value is the list of `FileNode`.
    */
-  buildFileTree(obj: object, level: number): FileNode[] {
+  buildFileTree(obj: {[key: string]: any}, level: number): FileNode[] {
     return Object.keys(obj).reduce<FileNode[]>((accumulator, key) => {
       const value = obj[key];
       const node = new FileNode();
diff --git a/src/material-examples/tree-nested-overview/tree-nested-overview-example.ts b/src/material-examples/tree-nested-overview/tree-nested-overview-example.ts
index 9fe9960edd12..2e93cde5ac45 100644
--- a/src/material-examples/tree-nested-overview/tree-nested-overview-example.ts
+++ b/src/material-examples/tree-nested-overview/tree-nested-overview-example.ts
@@ -84,7 +84,7 @@ export class FileDatabase {
    * Build the file structure tree. The `value` is the Json object, or a sub-tree of a Json object.
    * The return value is the list of `FileNode`.
    */
-  buildFileTree(obj: object, level: number): FileNode[] {
+  buildFileTree(obj: {[key: string]: any}, level: number): FileNode[] {
     return Object.keys(obj).reduce<FileNode[]>((accumulator, key) => {
       const value = obj[key];
       const node = new FileNode();
diff --git a/src/material-examples/tsconfig-build.json b/src/material-examples/tsconfig-build.json
index 8c3ce3b2747d..4a4e4c1adc66 100644
--- a/src/material-examples/tsconfig-build.json
+++ b/src/material-examples/tsconfig-build.json
@@ -10,6 +10,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "importHelpers": true,
     "module": "es2015",
     "moduleResolution": "node",
diff --git a/src/material-experimental/tsconfig-build.json b/src/material-experimental/tsconfig-build.json
index c022e3f7e963..0f506de7c51a 100644
--- a/src/material-experimental/tsconfig-build.json
+++ b/src/material-experimental/tsconfig-build.json
@@ -8,6 +8,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "importHelpers": true,
     "newLine": "lf",
     "module": "es2015",
diff --git a/src/material-moment-adapter/tsconfig-build.json b/src/material-moment-adapter/tsconfig-build.json
index 7d1ddb66e681..c73a5c413692 100644
--- a/src/material-moment-adapter/tsconfig-build.json
+++ b/src/material-moment-adapter/tsconfig-build.json
@@ -10,6 +10,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "importHelpers": true,
     "newLine": "lf",
     "module": "es2015",
diff --git a/src/universal-app/tsconfig-build.json b/src/universal-app/tsconfig-build.json
index 02997d9f473d..63c7dac01422 100644
--- a/src/universal-app/tsconfig-build.json
+++ b/src/universal-app/tsconfig-build.json
@@ -8,6 +8,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "module": "commonjs",
     "moduleResolution": "node",
     "outDir": ".",
diff --git a/src/universal-app/tsconfig-prerender.json b/src/universal-app/tsconfig-prerender.json
index 94b225fc3396..5ec5434fac82 100644
--- a/src/universal-app/tsconfig-prerender.json
+++ b/src/universal-app/tsconfig-prerender.json
@@ -7,6 +7,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "module": "commonjs",
     "moduleResolution": "node",
     "outDir": ".",
diff --git a/tsconfig.json b/tsconfig.json
index 25340ec4ed32..3b29a0f200a2 100644
--- a/tsconfig.json
+++ b/tsconfig.json
@@ -9,6 +9,7 @@
     "noUnusedParameters": true,
     "strictNullChecks": true,
     "strictFunctionTypes": true,
+    "noImplicitAny": true,
     "skipLibCheck": true,
     "target": "es2015",
     "lib": ["es5", "es2015", "dom"],