diff --git a/src/tree_interface.rs b/src/tree_interface.rs
index 271102414..7ac16da50 100644
--- a/src/tree_interface.rs
+++ b/src/tree_interface.rs
@@ -10,6 +10,7 @@ use crate::TskitError;
 use crate::TskitTypeAccess;
 use std::ptr::NonNull;
 
+#[derive(Debug)]
 pub struct TreeInterface {
     non_owned_pointer: NonNull<ll_bindings::tsk_tree_t>,
     num_nodes: tsk_size_t,
diff --git a/src/trees.rs b/src/trees.rs
index 56ce4e2b7..d38040b99 100644
--- a/src/trees.rs
+++ b/src/trees.rs
@@ -1,6 +1,5 @@
 use std::mem::MaybeUninit;
-use std::ops::Deref;
-use std::ops::DerefMut;
+use std::ops::{Deref, DerefMut};
 
 use crate::bindings as ll_bindings;
 use crate::error::TskitError;
@@ -22,7 +21,6 @@ use crate::TreeSequenceFlags;
 use crate::TskReturnValue;
 use crate::TskitTypeAccess;
 use crate::{tsk_id_t, tsk_size_t, TableCollection};
-use ll_bindings::tsk_tree_free;
 use std::ptr::NonNull;
 
 /// A Tree.
@@ -35,13 +33,106 @@ pub struct Tree {
     advanced: bool,
 }
 
-impl Drop for Tree {
-    fn drop(&mut self) {
-        let rv = unsafe { tsk_tree_free(&mut self.inner) };
+pub struct TreeIterator {
+    tree: ll_bindings::tsk_tree_t,
+    current_tree: i32,
+    advanced: bool,
+    num_nodes: tsk_size_t,
+    array_len: tsk_size_t,
+    flags: TreeFlags,
+}
+
+impl TreeIterator {
+    // FIXME: init if fallible!
+    fn new(treeseq: &TreeSequence, num_nodes: u64) -> Self {
+        let mut tree = MaybeUninit::<ll_bindings::tsk_tree_t>::uninit();
+        let rv = unsafe { ll_bindings::tsk_tree_init(tree.as_mut_ptr(), treeseq.as_ptr(), 0) };
         assert_eq!(rv, 0);
+        let tree = unsafe { tree.assume_init() };
+
+        Self {
+            tree,
+            current_tree: -1,
+            advanced: false,
+            num_nodes,
+            array_len: num_nodes + 1,
+            flags: 0.into(),
+        }
+    }
+    fn item(&mut self) -> NonOwningTree {
+        NonOwningTree::new(
+            NonNull::from(&mut self.tree),
+            self.num_nodes,
+            self.array_len,
+            self.flags,
+        )
+    }
+}
+
+#[derive(Debug)]
+#[repr(transparent)]
+pub struct NonOwningTree {
+    api: TreeInterface,
+}
+
+impl Deref for NonOwningTree {
+    type Target = TreeInterface;
+
+    fn deref(&self) -> &Self::Target {
+        &self.api
     }
 }
 
+impl NonOwningTree {
+    fn new(
+        tree: NonNull<ll_bindings::tsk_tree_t>,
+        num_nodes: tsk_size_t,
+        array_len: tsk_size_t,
+        flags: TreeFlags,
+    ) -> Self {
+        let api = TreeInterface::new(tree, num_nodes, array_len, flags);
+        Self { api }
+    }
+}
+
+impl Iterator for TreeIterator {
+    type Item = NonOwningTree;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let rv = if self.current_tree == 0 {
+            unsafe { ll_bindings::tsk_tree_first(&mut self.tree) }
+        } else {
+            unsafe { ll_bindings::tsk_tree_next(&mut self.tree) }
+        };
+        if rv == 0 {
+            self.advanced = false;
+            self.current_tree += 1;
+        } else if rv == 1 {
+            self.advanced = true;
+            self.current_tree += 1;
+        } else if rv < 0 {
+            panic_on_tskit_error!(rv);
+        }
+        if self.advanced {
+            Some(self.item())
+        } else {
+            None
+        }
+    }
+}
+
+impl Drop for TreeIterator {
+    fn drop(&mut self) {
+        unsafe { ll_bindings::tsk_tree_free(&mut self.tree) };
+    }
+}
+
+// Trait defining iteration over nodes.
+trait NodeIterator {
+    fn next_node(&mut self);
+    fn current_node(&mut self) -> Option<NodeId>;
+}
+
 impl Deref for Tree {
     type Target = TreeInterface;
     fn deref(&self) -> &Self::Target {
@@ -49,6 +140,13 @@ impl Deref for Tree {
     }
 }
 
+impl Drop for Tree {
+    fn drop(&mut self) {
+        let rv = unsafe { ll_bindings::tsk_tree_free(&mut self.inner) };
+        assert_eq!(rv, 0);
+    }
+}
+
 impl DerefMut for Tree {
     fn deref_mut(&mut self) -> &mut Self::Target {
         &mut self.api
@@ -341,6 +439,13 @@ impl TreeSequence {
         Ok(tree)
     }
 
+    /// Return an iterator over the trees.
+    pub fn trees(&self) -> impl Iterator<Item = impl Deref<Target = TreeInterface>> + '_ {
+        // TODO: should have a safe wrapper for this
+        let num_nodes = unsafe { (*(*self.as_ptr()).tables).nodes.num_rows };
+        TreeIterator::new(self, num_nodes)
+    }
+
     /// Get the list of samples as a vector.
     /// # Panics
     ///
@@ -651,6 +756,37 @@ pub(crate) mod test_trees {
         }
     }
 
+    #[test]
+    fn test_new_trees_iterator() {
+        let treeseq = treeseq_from_small_table_collection();
+        for tree in treeseq.trees() {
+            for n in tree.traverse_nodes(NodeTraversalOrder::Preorder) {
+                for p in tree.parents(n).unwrap() {
+                    println!("{:?}", p);
+                }
+            }
+        }
+
+        // NOTE: the following blocks make cargo valgrind crash,
+        // which is a sign of badness.
+        panic!("cargo valgrind will fail here");
+
+        // This is a safety sticking point:
+        // we cannot collect the iterable itself b/c
+        // the underlying tree memory is re-used.
+        let i = treeseq.trees();
+        let v = Vec::<_>::from_iter(i);
+        assert_eq!(v.len(), 2);
+        for i in v {
+            println!("{:?}", i.parent_array());
+        }
+
+        let v = treeseq.trees().collect::<Vec<_>>();
+        for i in v {
+            println!("{:?}", i.parent_array());
+        }
+    }
+
     #[should_panic]
     #[test]
     fn test_num_tracked_samples_not_tracking_samples() {