diff --git a/src/Functors.jl b/src/Functors.jl
index 65fb494..fa3ce9f 100644
--- a/src/Functors.jl
+++ b/src/Functors.jl
@@ -2,7 +2,7 @@ module Functors
 
 using MacroTools
 
-export @functor, fmap, fcollect
+export @functor, fmap, fmapstructure, fcollect
 
 include("functor.jl")
 
diff --git a/src/functor.jl b/src/functor.jl
index f351108..90eb0fa 100644
--- a/src/functor.jl
+++ b/src/functor.jl
@@ -13,7 +13,7 @@ function makefunctor(m::Module, T, fs = fieldnames(T))
     f in fs ? :(y[$(yᵢ += 1)]) : :(x.$f)
   end
   escfs = [:($f=x.$f) for f in fs]
-  
+
   @eval m begin
     $Functors.functor(::Type{<:$T}, x) = ($(escfs...),), y -> $T($(escargs...))
   end
@@ -44,21 +44,76 @@ Equivalent to `functor(x)[1]`.
 """
 children(x) = functor(x)[1]
 
-function fmap1(f, x)
+function _default_walk(f, x)
   func, re = functor(x)
   re(map(f, func))
 end
 
-# See https://github.com/FluxML/Functors.jl/issues/2 for a discussion regarding the need for
-# cache.
-function fmap(f, x; exclude = isleaf, cache = IdDict())
+"""
+    fmap(f, x; exclude = isleaf, walk = Functors._default_walk)
+
+A structure and type preserving `map` that works for all [`functor`](@ref)s.
+
+By default, traverses `x` recursively using [`functor`](@ref)
+and transforms every leaf node identified by `exclude` with `f`.
+
+For advanced customization of the traversal behaviour, pass a custom `walk` function of the form `(f', xs) -> ...`.
+This function walks (maps) over `xs` calling the continuation `f'` to continue traversal.
+
+# Examples
+```jldoctest
+julia> struct Foo; x; y; end
+
+julia> @functor Foo
+
+julia> struct Bar; x; end
+
+julia> @functor Bar
+
+julia> m = Foo(Bar([1,2,3]), (4, 5));
+
+julia> fmap(x -> 2x, m)
+Foo(Bar([2, 4, 6]), (8, 10))
+
+julia> fmap(string, m)
+Foo(Bar("[1, 2, 3]"), ("4", "5"))
+
+julia> fmap(string, m, exclude = v -> v isa Bar)
+Foo("Bar([1, 2, 3])", (4, 5))
+
+julia> fmap(x -> 2x, m, walk=(f, x) -> x isa Bar ? x : Functors._default_walk(f, x))
+Foo(Bar([1, 2, 3]), (8, 10))
+```
+"""
+function fmap(f, x; exclude = isleaf, walk = _default_walk, cache = IdDict())
   haskey(cache, x) && return cache[x]
-  y = exclude(x) ? f(x) : fmap1(x -> fmap(f, x, cache = cache, exclude = exclude), x)
+  y = exclude(x) ? f(x) : walk(x -> fmap(f, x, exclude = exclude, walk = walk, cache = cache), x)
   cache[x] = y
 
   return y
 end
 
+"""
+    fmapstructure(f, x; exclude = isleaf)
+
+Like [`fmap`](@ref), but doesn't preserve the type of custom structs. Instead, it returns a (potentially nested) `NamedTuple`.
+
+Useful for when the output must not contain custom structs.
+
+# Examples
+```jldoctest
+julia> struct Foo; x; y; end
+
+julia> @functor Foo
+
+julia> m = Foo([1,2,3], (4, 5));
+
+julia> fmapstructure(x -> 2x, m)
+(x = [2, 4, 6], y = (8, 10))
+```
+"""
+fmapstructure(f, x; kwargs...) = fmap(f, x; walk = (f, x) -> map(f, children(x)), kwargs...)
+
 """
     fcollect(x; exclude = v -> false)
 
@@ -68,7 +123,7 @@ and collecting the results into a flat array.
 Doesn't recurse inside branches rooted at nodes `v`
 for which `exclude(v) == true`.
 In such cases, the root `v` is also excluded from the result.
-By default, `exclude` always yields `false`. 
+By default, `exclude` always yields `false`.
 
 See also [`children`](@ref).
 
@@ -83,7 +138,7 @@ julia> struct Bar; x; end
 
 julia> @functor Bar
 
-julia> struct NoChildren; x; y; end 
+julia> struct NoChildren; x; y; end
 
 julia> m = Foo(Bar([1,2,3]), NoChildren(:a, :b))
 
@@ -98,7 +153,7 @@ julia> fcollect(m, exclude = v -> v isa Bar)
 2-element Vector{Any}:
  Foo(Bar([1, 2, 3]), NoChildren(:a, :b))
  NoChildren(:a, :b)
- 
+
 julia> fcollect(m, exclude = v -> Functors.isleaf(v))
 2-element Vector{Any}:
  Foo(Bar([1, 2, 3]), NoChildren(:a, :b))
diff --git a/test/basics.jl b/test/basics.jl
index 9476e4e..7f28513 100644
--- a/test/basics.jl
+++ b/test/basics.jl
@@ -45,6 +45,13 @@ end
   @test fmap(f, x; exclude = x -> x isa AbstractArray) == x
 end
 
+@testset "Walk" begin
+  model = Foo((0, Bar([1, 2, 3])), [4, 5])
+
+  model′ = fmapstructure(identity, model)
+  @test model′ == (; x=(0, (; x=[1, 2, 3])), y=[4, 5])
+end
+
 @testset "Property list" begin
   model = Baz(1, 2, 3)
   model′ = fmap(x -> 2x, model)