diff --git a/NEWS.md b/NEWS.md
index 01eebbdef9a66..3075be411973e 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1147,6 +1147,9 @@ Deprecated or removed
 
   * `signif` has been deprecated in favor of the `sigdigits` keyword argument to `round`.
 
+  * The fallback definition of `eltype` that returned `Any` for any type is deprecated.
+    Code should be restructured to avoid calling `eltype` on types that might not support it ([#26852]).
+
 Command-line option changes
 ---------------------------
 
diff --git a/base/abstractdict.jl b/base/abstractdict.jl
index 040b6e07d5ac4..c0723b1bed0b9 100644
--- a/base/abstractdict.jl
+++ b/base/abstractdict.jl
@@ -586,7 +586,7 @@ end
 
 function IdDict(kv)
     try
-        dict_with_eltype((K, V) -> IdDict{K, V}, kv, eltype(kv))
+        dict_with_eltype((K, V) -> IdDict{K, V}, kv, IteratorEltype(typeof(kv)) isa HasEltype ? eltype(kv) : Any)
     catch e
         if !applicable(start, kv) || !all(x->isa(x,Union{Tuple,Pair}),kv)
             throw(ArgumentError(
diff --git a/base/array.jl b/base/array.jl
index b5c652c3c8ba6..18169368c3086 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -84,7 +84,12 @@ julia> eltype(fill(0x1, (2,2)))
 UInt8
 ```
 """
-eltype(::Type) = Any
+function eltype(t::Type)
+    # TODO: change post-0.7
+    #throw(MethodError(eltype, (t,)))
+    depwarn("The fallback definition of `eltype` is deprecated; either define it for your type or avoid calling it on types that might not support it.", :eltype)
+    return Any
+end
 eltype(::Type{Bottom}) = throw(ArgumentError("Union{} does not have elements"))
 eltype(x) = eltype(typeof(x))
 
diff --git a/base/asyncmap.jl b/base/asyncmap.jl
index c8fec713bdb2f..cc9ea1d02ed4c 100644
--- a/base/asyncmap.jl
+++ b/base/asyncmap.jl
@@ -401,7 +401,8 @@ end
 
 # pass-through iterator traits to the iterable
 # on which the mapping function is being applied
-IteratorSize(itr::AsyncGenerator) = SizeUnknown()
+IteratorSize(::Type{AsyncGenerator}) = SizeUnknown()
+IteratorEltype(::Type{AsyncGenerator}) = EltypeUnknown()
 size(itr::AsyncGenerator) = size(itr.collector.enumerator)
 length(itr::AsyncGenerator) = length(itr.collector.enumerator)
 
diff --git a/base/compiler/abstractinterpretation.jl b/base/compiler/abstractinterpretation.jl
index 68299eb5385cb..c1ac38d46097d 100644
--- a/base/compiler/abstractinterpretation.jl
+++ b/base/compiler/abstractinterpretation.jl
@@ -350,7 +350,7 @@ function precise_container_type(@nospecialize(arg), @nospecialize(typ), vtypes::
         else
             return Any[ p for p in tti0.parameters ]
         end
-    elseif tti0 <: Array
+    elseif tti0 isa Type{<:Array{T}} where T
         return Any[Vararg{eltype(tti0)}]
     else
         return Any[abstract_iteration(typ, vtypes, sv)]
diff --git a/base/dict.jl b/base/dict.jl
index 61bc06a2f90de..3a4925c149213 100644
--- a/base/dict.jl
+++ b/base/dict.jl
@@ -134,7 +134,7 @@ Dict(ps::Pair...)                  = Dict(ps)
 
 function Dict(kv)
     try
-        dict_with_eltype((K, V) -> Dict{K, V}, kv, eltype(kv))
+        dict_with_eltype((K, V) -> Dict{K, V}, kv, IteratorEltype(typeof(kv)) isa HasEltype ? eltype(kv) : Any)
     catch e
         if !applicable(start, kv) || !all(x->isa(x,Union{Tuple,Pair}),kv)
             throw(ArgumentError("Dict(kv): kv needs to be an iterator of tuples or pairs"))
diff --git a/base/error.jl b/base/error.jl
index 35cde7fc8afa9..fa117f6fc016f 100644
--- a/base/error.jl
+++ b/base/error.jl
@@ -176,6 +176,7 @@ function next(ebo::ExponentialBackOff, state)
 end
 done(ebo::ExponentialBackOff, state) = state[1]<1
 length(ebo::ExponentialBackOff) = ebo.n
+eltype(::Type{ExponentialBackOff}) = Float64
 
 """
     retry(f::Function;  delays=ExponentialBackOff(), check=nothing) -> Function
diff --git a/base/essentials.jl b/base/essentials.jl
index b09df65a0e52e..e23bd5e9155ed 100644
--- a/base/essentials.jl
+++ b/base/essentials.jl
@@ -533,6 +533,7 @@ lastindex(v::SimpleVector) = length(v)
 start(v::SimpleVector) = 1
 next(v::SimpleVector,i) = (v[i],i+1)
 done(v::SimpleVector,i) = (length(v) < i)
+eltype(::Type{SimpleVector}) = Any
 keys(v::SimpleVector) = OneTo(length(v))
 isempty(v::SimpleVector) = (length(v) == 0)
 axes(v::SimpleVector) = (OneTo(length(v)),)
diff --git a/base/iterators.jl b/base/iterators.jl
index 59fa36816cbac..32443352a81b9 100644
--- a/base/iterators.jl
+++ b/base/iterators.jl
@@ -233,10 +233,8 @@ size(v::Pairs)    = size(v.itr)
 end
 @inline done(v::Pairs, state) = done(v.itr, state)
 
-eltype(::Type{Pairs{K, V}}) where {K, V} = Pair{K, V}
-
-IteratorSize(::Type{Pairs{<:Any, <:Any, I}}) where {I} = IteratorSize(I)
-IteratorEltype(::Type{Pairs{<:Any, <:Any, I}}) where {I} = IteratorEltype(I)
+IteratorSize(::Type{<:Pairs{<:Any, <:Any, I}}) where {I} = IteratorSize(I)
+IteratorEltype(::Type{<:Pairs{<:Any, <:Any, I}}) where {I} = IteratorEltype(I)
 
 reverse(v::Pairs) = Pairs(v.data, reverse(v.itr))
 
@@ -472,11 +470,11 @@ start(i::Rest) = i.st
 @propagate_inbounds next(i::Rest, st) = next(i.itr, st)
 done(i::Rest, st) = done(i.itr, st)
 
-eltype(::Type{Rest{I}}) where {I} = eltype(I)
-IteratorEltype(::Type{Rest{I,S}}) where {I,S} = IteratorEltype(I)
+eltype(::Type{<:Rest{I}}) where {I} = eltype(I)
+IteratorEltype(::Type{<:Rest{I}}) where {I} = IteratorEltype(I)
 rest_iteratorsize(a) = SizeUnknown()
 rest_iteratorsize(::IsInfinite) = IsInfinite()
-IteratorSize(::Type{Rest{I,S}}) where {I,S} = rest_iteratorsize(IteratorSize(I))
+IteratorSize(::Type{<:Rest{I}}) where {I} = rest_iteratorsize(IteratorSize(I))
 
 # Count -- infinite counting
 
@@ -897,7 +895,10 @@ flatten_iteratorsize(::Union{HasShape, HasLength}, ::Type{<:Tuple}) = SizeUnknow
 flatten_iteratorsize(::Union{HasShape, HasLength}, ::Type{<:Number}) = HasLength()
 flatten_iteratorsize(a, b) = SizeUnknown()
 
-IteratorSize(::Type{Flatten{I}}) where {I} = flatten_iteratorsize(IteratorSize(I), eltype(I))
+_flatten_iteratorsize(sz, ::EltypeUnknown, I) = SizeUnknown()
+_flatten_iteratorsize(sz, ::HasEltype, I) = flatten_iteratorsize(sz, eltype(I))
+
+IteratorSize(::Type{Flatten{I}}) where {I} = _flatten_iteratorsize(IteratorSize(I), IteratorEltype(I), I)
 
 function flatten_length(f, T::Type{<:NTuple{N,Any}}) where {N}
     fieldcount(T)*length(f.it)
@@ -968,6 +969,8 @@ function IteratorSize(::Type{PartitionIterator{T}}) where {T}
     partition_iteratorsize(IteratorSize(T))
 end
 
+IteratorEltype(::Type{<:PartitionIterator{T}}) where {T} = IteratorEltype(T)
+
 function length(itr::PartitionIterator)
     l = length(itr.c)
     return div(l, itr.n) + ((mod(l, itr.n) > 0) ? 1 : 0)
diff --git a/base/reflection.jl b/base/reflection.jl
index 18e675a25d130..4697cd2452a8a 100644
--- a/base/reflection.jl
+++ b/base/reflection.jl
@@ -684,6 +684,7 @@ isempty(m::MethodList) = isempty(m.ms)
 start(m::MethodList) = start(m.ms)
 done(m::MethodList, s) = done(m.ms, s)
 next(m::MethodList, s) = next(m.ms, s)
+eltype(::Type{MethodList}) = Method
 
 function MethodList(mt::Core.MethodTable)
     ms = Method[]
diff --git a/base/reshapedarray.jl b/base/reshapedarray.jl
index 3ac1c7cac616f..aebf17bb120e7 100644
--- a/base/reshapedarray.jl
+++ b/base/reshapedarray.jl
@@ -35,6 +35,7 @@ start(R::ReshapedArrayIterator) = start(R.iter)
     ReshapedIndex(item), inext
 end
 length(R::ReshapedArrayIterator) = length(R.iter)
+eltype(::Type{<:ReshapedArrayIterator{I}}) where {I} = @isdefined(I) ? ReshapedIndex{eltype(I)} : Any
 
 """
     reshape(A, dims...) -> R
diff --git a/base/task.jl b/base/task.jl
index 9c89a78165c3a..e46f3426049c0 100644
--- a/base/task.jl
+++ b/base/task.jl
@@ -37,6 +37,7 @@ isempty(c::CompositeException) = isempty(c.exceptions)
 start(c::CompositeException) = start(c.exceptions)
 next(c::CompositeException, state) = next(c.exceptions, state)
 done(c::CompositeException, state) = done(c.exceptions, state)
+eltype(::Type{CompositeException}) = Any
 
 function showerror(io::IO, ex::CompositeException)
     if !isempty(ex)
diff --git a/base/weakkeydict.jl b/base/weakkeydict.jl
index fb153d500d96e..23626c15cdf0d 100644
--- a/base/weakkeydict.jl
+++ b/base/weakkeydict.jl
@@ -58,7 +58,7 @@ WeakKeyDict(ps::Pair...)                            = WeakKeyDict{Any,Any}(ps)
 
 function WeakKeyDict(kv)
     try
-        Base.dict_with_eltype((K, V) -> WeakKeyDict{K, V}, kv, eltype(kv))
+        Base.dict_with_eltype((K, V) -> WeakKeyDict{K, V}, kv, IteratorEltype(typeof(kv)) isa HasEltype ? eltype(kv) : Any)
     catch e
         if !applicable(start, kv) || !all(x->isa(x,Union{Tuple,Pair}),kv)
             throw(ArgumentError("WeakKeyDict(kv): kv needs to be an iterator of tuples or pairs"))
diff --git a/stdlib/Distributed/src/cluster.jl b/stdlib/Distributed/src/cluster.jl
index 4d47d5fcfc2c3..110a6e02f4827 100644
--- a/stdlib/Distributed/src/cluster.jl
+++ b/stdlib/Distributed/src/cluster.jl
@@ -42,8 +42,7 @@ mutable struct WorkerConfig
 
     function WorkerConfig()
         wc = new()
-        for n in 1:length(WorkerConfig.types)
-            T = eltype(fieldtype(WorkerConfig, n))
+        for n in 1:fieldcount(WorkerConfig)
             setfield!(wc, n, nothing)
         end
         wc
diff --git a/stdlib/Random/src/Random.jl b/stdlib/Random/src/Random.jl
index ef79ef62e3138..cc84bb55ae226 100644
--- a/stdlib/Random/src/Random.jl
+++ b/stdlib/Random/src/Random.jl
@@ -132,7 +132,7 @@ struct SamplerTrivial{T,E} <: Sampler{E}
     self::T
 end
 
-SamplerTrivial(x::T) where {T} = SamplerTrivial{T,eltype(T)}(x)
+SamplerTrivial(x::T) where {T} = SamplerTrivial{T,Any}(x)
 
 Sampler(::AbstractRNG, x, ::Repetition) = SamplerTrivial(x)
 
@@ -144,14 +144,14 @@ struct SamplerSimple{T,S,E} <: Sampler{E}
     data::S
 end
 
-SamplerSimple(x::T, data::S) where {T,S} = SamplerSimple{T,S,eltype(T)}(x, data)
+SamplerSimple(x::T, data::S) where {T,S} = SamplerSimple{T,S,Any}(x, data)
 
 Base.getindex(sp::SamplerSimple) = sp.self
 
 # simple sampler carrying a (type) tag T and data
 struct SamplerTag{T,S,E} <: Sampler{E}
     data::S
-    SamplerTag{T}(s::S) where {T,S} = new{T,S,eltype(T)}(s)
+    SamplerTag{T}(s::S) where {T,S} = new{T,S,Any}(s)
 end
 
 
diff --git a/test/iterators.jl b/test/iterators.jl
index 801d666e8a105..224211ec1a679 100644
--- a/test/iterators.jl
+++ b/test/iterators.jl
@@ -66,7 +66,9 @@ end
 # ----
 let s = "hello"
     _, st = next(s, start(s))
-    @test collect(rest(s, st)) == ['e','l','l','o']
+    c = collect(rest(s, st))
+    @test c == ['e','l','l','o']
+    @test c isa Vector{Char}
 end
 
 @test_throws MethodError collect(rest(countfrom(1), 5))
@@ -452,6 +454,7 @@ end
         @test values(d) == A
         @test Base.IteratorSize(d) == Base.HasLength()
         @test Base.IteratorEltype(d) == Base.HasEltype()
+        @test Base.IteratorSize(pairs([1 2;3 4])) isa Base.HasShape{2}
         @test isempty(d) || haskey(d, first(keys(d)))
         @test collect(v for (k, v) in d) == vec(collect(A))
         if A isa NamedTuple
diff --git a/test/missing.jl b/test/missing.jl
index 6825c07bbe74b..7685134272272 100644
--- a/test/missing.jl
+++ b/test/missing.jl
@@ -358,7 +358,8 @@ end
     @test collect(x) isa Vector{Int}
 
     x = skipmissing(v for v in [missing, 1, missing, 2, 4])
-    @test eltype(x) === Any
+    # TODO: enable in v0.7
+    #@test_throws MethodError eltype(x)
     @test collect(x) == [1, 2, 4]
     @test collect(x) isa Vector{Int}
 end