diff --git a/Project.toml b/Project.toml
index 653c550..1dba91c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -12,8 +12,9 @@ julia = "1.6"
 
 [extras]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Test", "Documenter", "Zygote"]
+test = ["Test", "Documenter", "StaticArrays", "Zygote"]
diff --git a/docs/src/api.md b/docs/src/api.md
index 59a639e..5d1c200 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -9,6 +9,16 @@ Functors.children
 Functors.isleaf
 ```
 
+```@docs
+Functors.AbstractWalk
+Functors.DefaultWalk
+Functors.StructuralWalk
+Functors.ExcludeWalk
+Functors.CachedWalk
+Functors.CollectWalk
+Functors.AnonymousWalk
+```
+
 ```@docs
 Functors.fmapstructure
 Functors.fcollect
diff --git a/src/Functors.jl b/src/Functors.jl
index fe9b399..5d357ca 100644
--- a/src/Functors.jl
+++ b/src/Functors.jl
@@ -3,6 +3,8 @@ module Functors
 export @functor, @flexiblefunctor, fmap, fmapstructure, fcollect
 
 include("functor.jl")
+include("walks.jl")
+include("maps.jl")
 include("base.jl")
 
 ###
@@ -102,7 +104,8 @@ Equivalent to `functor(x)[1]`.
 children
 
 """
-    fmap(f, x; exclude = Functors.isleaf, walk = Functors._default_walk)
+    fmap(f, x, ys...; exclude = Functors.isleaf, walk = Functors.DefaultWalk()[, prune])
+    fmap(walk, f, x, ys...)
 
 A structure and type preserving `map`.
 
@@ -176,12 +179,23 @@ Foo("Bar([1, 2, 3])", (4, 5, "Bar(Foo(6, 7))"))
 To recurse into custom types without reconstructing them afterwards,
 use [`fmapstructure`](@ref).
 
-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.
+For advanced customization of the traversal behaviour,
+pass a custom `walk` function that subtypes [`Functors.AbstractWalk`](ref).
+The form `fmap(walk, f, x, ys...)` can be called for custom walks.
+The simpler form `fmap(f, x, ys...; walk = mywalk)` will wrap `mywalk` in
+[`ExcludeWalk`](@ref) then [`CachedWalk`](@ref).
 
 ```jldoctest withfoo
-julia> fmap(x -> 10x, m, walk=(f, x) -> x isa Bar ? x : Functors._default_walk(f, x))
-Foo(Bar([1, 2, 3]), (40, 50, Bar(Foo(6, 7))))
+julia> struct MyWalk <: Functors.AbstractWalk end
+
+julia> (::MyWalk)(recurse, x) = x isa Bar ? "hello" :
+                                            Functors.DefaultWalk()(recurse, x)
+
+julia> fmap(x -> 10x, m; walk = MyWalk())
+Foo("hello", (40, 50, "hello"))
+
+julia> fmap(MyWalk(), x -> 10x, m)
+Foo("hello", (4, 5, "hello"))
 ```
 
 The behaviour when the same node appears twice can be altered by giving a value
diff --git a/src/functor.jl b/src/functor.jl
index c89fd03..9c8cf78 100644
--- a/src/functor.jl
+++ b/src/functor.jl
@@ -34,81 +34,6 @@ isleaf(x) = children(x) === ()
 
 children(x) = functor(x)[1]
 
-function _default_walk(f, x)
-  func, re = functor(x)
-  re(map(f, func))
-end
-
-usecache(::AbstractDict, x) = isleaf(x) ? anymutable(x) : ismutable(x)
-usecache(::Nothing, x) = false
-
-@generated function anymutable(x::T) where {T}
-  ismutabletype(T) && return true
-  subs =  [:(anymutable(getfield(x, $f))) for f in QuoteNode.(fieldnames(T))]
-  return Expr(:(||), subs...)
-end
-
-struct NoKeyword end
-
-function fmap(f, x; exclude = isleaf, walk = _default_walk, cache = anymutable(x) ? IdDict() : nothing, prune = NoKeyword())
-  if usecache(cache, x) && haskey(cache, x)
-    return prune isa NoKeyword ? cache[x] : prune
-  end
-  ret = if exclude(x)
-    f(x)
-  else
-    walk(x -> fmap(f, x; exclude, walk, cache, prune), x)
-  end
-  if usecache(cache, x)
-    cache[x] = ret
-  end
-  ret
-end  
-
-###
-### Extras
-###
-
-fmapstructure(f, x; kwargs...) = fmap(f, x; walk = (f, x) -> map(f, children(x)), kwargs...)
-
-function fcollect(x; output = [], cache = Base.IdSet(), exclude = v -> false)
-    # note: we don't have an `OrderedIdSet`, so we use an `IdSet` for the cache
-    # (to ensure we get exactly 1 copy of each distinct array), and a usual `Vector`
-    # for the results, to preserve traversal order (important downstream!).
-    x in cache && return output
-    if !exclude(x)
-      push!(cache, x)
-      push!(output, x)
-      foreach(y -> fcollect(y; cache=cache, output=output, exclude=exclude), children(x))
-    end
-    return output
-end
-
-###
-### Vararg forms
-###
-
-function fmap(f, x, ys...; exclude = isleaf, walk = _default_walk, cache = anymutable(x) ? IdDict() : nothing, prune = NoKeyword())
-  if usecache(cache, x) && haskey(cache, x)
-    return prune isa NoKeyword ? cache[x] : prune
-  end
-  ret = if exclude(x)
-    f(x, ys...)
-  else
-    walk((xy...,) -> fmap(f, xy...; exclude, walk, cache, prune), x, ys...)
-  end
-  if usecache(cache, x)
-    cache[x] = ret
-  end
-  ret
-end
-
-function _default_walk(f, x, ys...)
-  func, re = functor(x)
-  yfuncs = map(y -> functor(typeof(x), y)[1], ys)
-  re(map(f, func, yfuncs...))
-end
-
 ###
 ### FlexibleFunctors.jl
 ###
diff --git a/src/maps.jl b/src/maps.jl
new file mode 100644
index 0000000..e5e89e4
--- /dev/null
+++ b/src/maps.jl
@@ -0,0 +1,17 @@
+fmap(walk::AbstractWalk, f, x, ys...) = walk((xs...) -> fmap(walk, f, xs...), x, ys...)
+
+function fmap(f, x, ys...; exclude = isleaf,
+                           walk = DefaultWalk(),
+                           cache = IdDict(),
+                           prune = NoKeyword())
+  _walk = ExcludeWalk(AnonymousWalk(walk), f, exclude)
+  if !isnothing(cache)
+    _walk = CachedWalk(_walk, prune, cache)
+  end
+  fmap(_walk, f, x, ys...)
+end
+
+fmapstructure(f, x; kwargs...) = fmap(f, x; walk = StructuralWalk(), kwargs...)
+
+fcollect(x; exclude = v -> false) =
+  fmap(ExcludeWalk(CollectWalk(), _ -> nothing, exclude), _ -> nothing, x)
diff --git a/src/walks.jl b/src/walks.jl
new file mode 100644
index 0000000..79429f9
--- /dev/null
+++ b/src/walks.jl
@@ -0,0 +1,162 @@
+"""
+    AbstractWalk
+
+Any walk for use with [`fmap`](@ref) should inherit from this type.
+A walk subtyping `AbstractWalk` must satisfy the walk function interface:
+```julia
+struct MyWalk <: AbstractWalk end
+
+function (::MyWalk)(recurse, x, ys...)
+  # implement this
+end
+```
+The walk function is called on a node `x` in a Functors tree.
+It may also be passed associated nodes `ys...` in other Functors trees.
+The walk function recurses further into `(x, ys...)` by calling
+`recurse` on the child nodes.
+The choice of which nodes to recurse and in what order is custom to the walk.
+"""
+abstract type AbstractWalk end
+
+"""
+    AnonymousWalk(walk_fn)
+
+Wrap a `walk_fn` so that `AnonymousWalk(walk_fn) isa AbstractWalk`.
+This type only exists for backwards compatability and should be directly used.
+Attempting to wrap an existing `AbstractWalk` is a no-op (i.e. it is not wrapped).
+"""
+struct AnonymousWalk{F} <: AbstractWalk
+  walk::F
+
+  function AnonymousWalk(walk::F) where F
+    Base.depwarn("Wrapping a custom walk function as an `AnonymousWalk`. Future versions will only support custom walks that explicitly subtyle `AbstractWalk`.", :AnonymousWalk)
+    return new{F}(walk)
+  end
+end
+# do not wrap an AbstractWalk
+AnonymousWalk(walk::AbstractWalk) = walk
+
+(walk::AnonymousWalk)(recurse, x, ys...) = walk.walk(recurse, x, ys...)
+
+"""
+    DefaultWalk()
+
+The default walk behavior for Functors.jl.
+Walks all the [`Functors.children`](@ref) of trees `(x, ys...)` based on
+the structure of `x`.
+The resulting mapped child nodes are restructured into the type of `x`.
+
+See [`fmap`](@ref) for more information.
+"""
+struct DefaultWalk <: AbstractWalk end
+
+function (::DefaultWalk)(recurse, x, ys...)
+  func, re = functor(x)
+  yfuncs = map(y -> functor(typeof(x), y)[1], ys)
+  re(map(recurse, func, yfuncs...))
+end
+
+"""
+    StructuralWalk()
+
+A structural variant of [`Functors.DefaultWalk`](@ref).
+The recursion behavior is identical, but the mapped children are not restructured.
+
+See [`fmapstructure`](@ref) for more information.
+"""
+struct StructuralWalk <: AbstractWalk end
+
+(::StructuralWalk)(recurse, x) = map(recurse, children(x))
+
+"""
+    ExcludeWalk(walk, fn, exclude)
+
+A walk that recurses nodes `(x, ys...)` according to `walk`,
+except when `exclude(x)` is true.
+Then, `fn(x, ys...)` is applied instead of recursing further.
+
+Typically wraps an existing `walk` for use with [`fmap`](@ref).
+"""
+struct ExcludeWalk{T, F, G} <: AbstractWalk
+  walk::T
+  fn::F
+  exclude::G
+end
+
+(walk::ExcludeWalk)(recurse, x, ys...) =
+  walk.exclude(x) ? walk.fn(x, ys...) : walk.walk(recurse, x, ys...)
+
+struct NoKeyword end
+
+usecache(::Union{AbstractDict, AbstractSet}, x) =
+  isleaf(x) ? anymutable(x) : ismutable(x)
+usecache(::Nothing, x) = false
+
+@generated function anymutable(x::T) where {T}
+  ismutabletype(T) && return true
+  subs =  [:(anymutable(getfield(x, $f))) for f in QuoteNode.(fieldnames(T))]
+  return Expr(:(||), subs...)
+end
+
+"""
+    CachedWalk(walk[; prune])
+
+A walk that recurses nodes `(x, ys...)` according to `walk` and storing the
+output of the recursion in a cache indexed by `x` (based on object ID).
+Whenever the cache already contains `x`, either:
+- `prune` is specified, then it is returned, or
+- `prune` is unspecified, and the previously cached recursion of `(x, ys...)`
+  returned.
+
+Typically wraps an existing `walk` for use with [`fmap`](@ref).
+"""
+struct CachedWalk{T, S} <: AbstractWalk
+  walk::T
+  prune::S
+  cache::IdDict{Any, Any}
+end
+CachedWalk(walk; prune = NoKeyword(), cache = IdDict()) =
+  CachedWalk(walk, prune, cache)
+
+function (walk::CachedWalk)(recurse, x, ys...)
+  should_cache = usecache(walk.cache, x)
+  if should_cache && haskey(walk.cache, x)
+    return walk.prune isa NoKeyword ? walk.cache[x] : walk.prune
+  else
+    ret = walk.walk(recurse, x, ys...)
+    if should_cache
+      walk.cache[x] = ret
+    end
+    return ret
+  end
+end
+
+"""
+    CollectWalk()
+
+A walk that recurses into a node `x` via [`Functors.children`](@ref),
+storing the recursion history in a cache.
+The resulting ordered recursion history is returned.
+
+See [`fcollect`](@ref) for more information.
+"""
+struct CollectWalk <: AbstractWalk
+  cache::Base.IdSet{Any}
+  output::Vector{Any}
+end
+CollectWalk() = CollectWalk(Base.IdSet(), Any[])
+
+# note: we don't have an `OrderedIdSet`, so we use an `IdSet` for the cache
+# (to ensure we get exactly 1 copy of each distinct array), and a usual `Vector`
+# for the results, to preserve traversal order (important downstream!).
+function (walk::CollectWalk)(recurse, x)
+  if usecache(walk.cache, x) && (x in walk.cache)
+    return walk.output
+  end
+  # to exclude, we wrap this walk in ExcludeWalk
+  usecache(walk.cache, x) && push!(walk.cache, x)
+  push!(walk.output, x)
+  map(recurse, children(x))
+
+  return walk.output
+end
diff --git a/test/basics.jl b/test/basics.jl
index 625e673..5aeba77 100644
--- a/test/basics.jl
+++ b/test/basics.jl
@@ -85,9 +85,7 @@ end
   @test m5f.x === m5f.y
   @test m5f.x !== m5f.z
 
-  @testset "usecache" begin
-    d = IdDict()
-
+  @testset "usecache ($d)" for d in [IdDict(), Base.IdSet()]
     # Leaf types:
     @test usecache(d, [1,2])
     @test !usecache(d, 4.0)
@@ -101,9 +99,9 @@ end
 
     @test !usecache(d, (5, [6.0]'))  # contains mutable
     @test !usecache(d, (x = [1,2,3], y = 4))
-    
+
     usecache(d, OneChild3([1,2], 3, nothing))  # mutable isn't a child, do we care?
-    
+
     # No dictionary:
     @test !usecache(nothing, [1,2])
     @test !usecache(nothing, 3)
@@ -173,6 +171,14 @@ end
   m2 = [1, 2, 3]
   m3 = Foo(m1, m2)
   @test all(fcollect(m3) .=== [m3, m1, m2])
+
+  m1 = [1, 2, 3]
+  m2 = SVector{length(m1)}(m1)
+  m2′ = SVector{length(m1)}(m1)
+  m3 = Foo(m1, m1)
+  m4 = Foo(m2, m2′)
+  @test all(fcollect(m3) .=== [m3, m1])
+  @test all(fcollect(m4) .=== [m4, m2, m2′])
 end
 
 ###
diff --git a/test/runtests.jl b/test/runtests.jl
index 7bc7c88..86f1e6b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,7 @@
 using Functors, Test
 using Zygote
 using LinearAlgebra
+using StaticArrays
 
 @testset "Functors.jl" begin