diff --git a/.gitignore b/.gitignore
index e4fecbbe..952f7cea 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,4 @@
 Manifest.toml
 .vscode/
+docs/build/
+.DS_Store
diff --git a/Project.toml b/Project.toml
index 7422f28c..4920eaa9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -12,7 +12,7 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
 ChainRulesCore = "1"
-Functors = "0.4"
+Functors = "0.4.9"
 Statistics = "1"
 Zygote = "0.6.40"
 julia = "1.6"
diff --git a/docs/.DS_Store b/docs/.DS_Store
new file mode 100644
index 00000000..e1455310
Binary files /dev/null and b/docs/.DS_Store differ
diff --git a/docs/make.jl b/docs/make.jl
index 8d0504b2..47d64137 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -2,7 +2,7 @@ using Documenter, Optimisers, Zygote, StaticArrays, Functors
 
 DocMeta.setdocmeta!(Optimisers, :DocTestSetup, :(using Optimisers); recursive = true)
 
-makedocs(modules = [Optimisers, Zygote, StaticArrays, Functors],
+makedocs(modules = [Optimisers],
          doctest = false,
          sitename = "Optimisers.jl",
          pages = ["Home" => "index.md",
diff --git a/docs/src/api.md b/docs/src/api.md
index 661f83bc..296057bf 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -51,6 +51,7 @@ To further restrict this by ignoring some fields of a layer type, define `traina
 ```@docs
 Optimisers.trainable
 Optimisers.isnumeric
+Optimisers.maywrite
 ```
 
 Such restrictions are also obeyed by this function for flattening a model:
@@ -58,6 +59,7 @@ Such restrictions are also obeyed by this function for flattening a model:
 ```@docs
 Optimisers.destructure
 Optimisers.Restructure
+Optimisers.trainables
 ```
 
 ## Rule Definition
@@ -68,4 +70,16 @@ Optimisers.init
 Optimisers.@..
 Optimisers.@lazy
 Optimisers.adjust(::AbstractRule, ::Real)
+Optimisers.@def
+```
+
+## KeyPath
+
+A `KeyPath` is a sequence of keys that can be used to access a value within a nested structure.
+It is defined in Functors.jl and re-exported by Optimisers.jl here for convenience.
+
+```@docs
+Functors.KeyPath
+Functors.haskeypath
+Functors.getkeypath
 ```
diff --git a/docs/src/index.md b/docs/src/index.md
index 38d7b93e..30ef5c45 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -290,3 +290,29 @@ flat, re = destructure(params)
 end
 ```
 
+## Collecting all trainable parameters
+
+Sometimes it is useful to collect all trainable parameters in a model,
+similarly to what [`destructure`](@ref Optimisers.destructure) does but without
+concatenating the arrays into a flat vector.
+This is done by [`trainables`](@ref Optimisers.trainables), which returns a list of arrays:
+
+```julia
+julia> using Flux, Optimisers
+
+julia> model = Chain(Dense(2 => 3, tanh), BatchNorm(3), Dense(3 => 2));
+
+julia> trainables(model)
+6-element Vector{AbstractArray}:
+ Float32[0.5756773 -0.1975264; 0.4723181 -0.7546912; -0.91631395 0.07392061]
+ Float32[0.0, 0.0, 0.0]
+ Float32[0.0, 0.0, 0.0]
+ Float32[1.0, 1.0, 1.0]
+ Float32[-0.8764882 0.40812716 0.1919528; -0.9123545 -0.4462516 0.6751252]
+ Float32[0.0, 0.0]
+
+julia> l2reg(model) = sum([sum(abs2,p) for p in trainables(model)]);
+
+julia> g = gradient(l2reg, model)[1];
+```
+Notice that the `BatchNorm` layer has two trainable parameters, `γ` and `β`, which are included in the list, while the `μ ` and `σ²` buffers are not.
diff --git a/src/Optimisers.jl b/src/Optimisers.jl
index efe28697..2e115c40 100644
--- a/src/Optimisers.jl
+++ b/src/Optimisers.jl
@@ -1,16 +1,24 @@
 module Optimisers
 
-using Functors: functor, fmap, isleaf, @functor, fmapstructure, children, AbstractWalk
+using Functors: functor, fmap, fmap_with_path, 
+                KeyPath, haskeypath, getkeypath,
+                isleaf, @functor, fmapstructure, children, AbstractWalk
 using LinearAlgebra
 
 include("interface.jl")
 export AbstractRule
 
+include("utils.jl")
+
 include("adjust.jl")
 
 include("destructure.jl")
 export destructure
 
+include("trainables.jl")
+export trainables
+export KeyPath, haskeypath, getkeypath # from Functors.jl
+
 include("rules.jl")
 export Descent, Adam, Momentum, Nesterov, Rprop, RMSProp,
        AdaGrad, AdaMax, AdaDelta, AMSGrad, NAdam, AdamW, RAdam, OAdam, AdaBelief,
diff --git a/src/destructure.jl b/src/destructure.jl
index a73e36a6..a6284522 100644
--- a/src/destructure.jl
+++ b/src/destructure.jl
@@ -66,19 +66,19 @@ function _flatten(x)
   isnumeric(x) && return vcat(_vec(x)), 0, length(x)  # trivial case
   arrays = AbstractVector[]
   len = Ref(0)
-  off = fmap(x; exclude = isnumeric, walk = _TrainableStructWalk()) do y
+  off = fmap(x; exclude = isnumeric, walk = TrainableStructWalk()) do y
     push!(arrays, _vec(y))
     o = len[]
     len[] = o + length(y)
     o
   end
   isempty(arrays) && return Bool[], off, 0
-  reduce(vcat, arrays), off, len[]
+  return reduce(vcat, arrays), off, len[]
 end
 
-struct _TrainableStructWalk <: AbstractWalk end
+struct TrainableStructWalk <: AbstractWalk end
 
-(::_TrainableStructWalk)(recurse, x) = map(recurse, _trainable(x))
+(::TrainableStructWalk)(recurse, x) = mapvalue(recurse, _trainable(x))
 
 _vec(x::Number) = LinRange(x,x,1)
 _vec(x::AbstractArray) = vec(x)
@@ -174,3 +174,4 @@ function ChainRulesCore.rrule(::typeof(_maybewarn))
   @warn "second derivatives of destructure may not work yet, sorry!" maxlog=3
   nothing, _ -> (NoT,)
 end
+
diff --git a/src/interface.jl b/src/interface.jl
index 29c1db60..ac9b90bc 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -45,7 +45,7 @@ function _setup(rule, x; cache)
       cache[x] = ℓ
     end
   else
-    valuemap(xᵢ -> _setup(rule, xᵢ; cache), _trainable(x))
+    mapvalue(xᵢ -> _setup(rule, xᵢ; cache), _trainable(x))
   end
 end
 
@@ -82,7 +82,7 @@ function _update!(tree, x; grads, params)
   haskey(params, (tree,x)) && return params[(tree,x)]
   isbits(tree) && return x  # means () is not cached, and also (((),),)
   x′, re = functor(x)
-  x′′ = re(valuemap((tᵢ, xᵢ) -> _update!(tᵢ, xᵢ; grads, params), tree, x′))
+  x′′ = re(mapvalue((tᵢ, xᵢ) -> _update!(tᵢ, xᵢ; grads, params), tree, x′))
   if ismutable(x′′)
     params[(tree,x)] = x′′
   else  # no ties to preserve between immutable structs, right?
@@ -115,7 +115,7 @@ function _grads!(dict::IdDict, tree, x, x̄s...)
   # functor(typeof(tree), base(x̄)), for things like Transpose
   x̄s′ = map(x̄ -> functor(typeof(x), base(x̄))[1], x̄s)
   x′, _ = functor(typeof(x), x)
-  valueforeach((tᵢ, xᵢ, x̄sᵢ...) -> _grads!(dict, tᵢ, xᵢ, x̄sᵢ...), tree, x′, x̄s′...)
+  foreachvalue((tᵢ, xᵢ, x̄sᵢ...) -> _grads!(dict, tᵢ, xᵢ, x̄sᵢ...), tree, x′, x̄s′...)
 end
 
 # default all rules to first order calls
@@ -167,11 +167,12 @@ and `trainable(x)` must contain a subset of these.
 """
 trainable(x) = functor(x)[1]
 
+# like trainable(x), but also tries to output non-trainable children giving value nothing
 _trainable(x) = _trainable(functor(x)[1], trainable(x))
 _trainable(ch::NamedTuple, tr::NamedTuple) = merge(map(_ -> nothing, ch), tr)
 _trainable(ch::Tuple{Vararg{Any,N}}, tr::Tuple{Vararg{Any,N}}) where N = tr
 _trainable(ch::AbstractArray, tr::AbstractArray) = tr
-_trainable(ch::Dict, tr::Dict) = merge(valuemap(_ -> nothing, ch), tr)
+_trainable(ch::Dict, tr::Dict) = merge(mapvalue(_ -> nothing, ch), tr)
 
 function _trainable(ch::NamedTuple, tr::Tuple)  # for old Flux-style no-names tuple
   @warn "trainable(x) should now return a NamedTuple with the field names, not a Tuple" maxlog=3
@@ -179,14 +180,6 @@ function _trainable(ch::NamedTuple, tr::Tuple)  # for old Flux-style no-names tu
 end
 
 
-valuemap(f, x...) = map(f, x...)
-valuemap(f, x::Dict, ys...) = Dict(k => f(v, (get(y, k, nothing) for y in ys)...) for (k,v) in x)
-valueforeach(f, x...) = foreach(f, x...)
-valueforeach(f, x::Dict, ys...) = foreach(pairs(x)) do (k, v)
-  f(v, (get(y, k, nothing) for y in ys)...)
-end
-
-
 ###
 ### rule definition helpers
 ###
diff --git a/src/trainables.jl b/src/trainables.jl
new file mode 100644
index 00000000..80059dd7
--- /dev/null
+++ b/src/trainables.jl
@@ -0,0 +1,124 @@
+
+"""
+    trainables(x, path = false)
+
+Return an iterable over all the trainable parameters in `x`, that is all the numerical
+arrays (see [`isnumeric`](@ref Optimisers.isnumeric)) which are reachable through [`trainable`](@ref Optimisers.trainable).
+
+Parameters appearing multiple times in the model (tied weights) will be present only once in the output.
+
+If `path = false`, the output is a list of numerical arrays.
+
+If `path = true`, the output is a list of `(KeyPath, AbstractArray)` pairs, where [`KeyPath`](@ref Functors.KeyPath) is a type
+representing the path to the array in the original structure.
+
+See also [`destructure`](@ref) for a similar operation that returns a single flat vector instead.
+
+# Examples
+
+```jldoctest
+julia> struct MyLayer
+         w
+         b
+       end
+
+julia> Functors.@functor MyLayer
+
+julia> Optimisers.trainable(x::MyLayer) = (; w = x.w,) # only w is trainable in this example
+
+julia> x = MyLayer([1.0,2.0,3.0], [4.0,5.0,6.0]);
+
+julia> trainables(x)
+1-element Vector{AbstractArray}:
+ [1.0, 2.0, 3.0]
+
+ julia> x = MyLayer((a=[1.0,2.0], b=[3.0]), [4.0,5.0,6.0]);
+
+ julia> trainables(x) # collects nested parameters
+ 2-element Vector{AbstractArray}:
+ [1.0, 2.0]
+ [3.0]
+```
+
+```jldoctest
+julia> x = (a = [1.0,2.0], b = (Dict("c" => [3.0, 4.0], "d" => 5.0), [6.0,7.0]));
+
+julia> for (kp, y) in trainables(x, path = true)
+           println(kp, " => ", y)
+       end
+KeyPath(:a,) => [1.0, 2.0]
+KeyPath(:b, 1, "c") => [3.0, 4.0]
+KeyPath(:b, 2) => [6.0, 7.0]
+
+julia> getkeypath(x, KeyPath(:b, 1, "c"))
+2-element Vector{Float64}:
+ 3.0
+ 4.0
+```
+"""
+function trainables(x; path = false)
+    if path
+        return _trainables_with_path(x)
+    else
+        return _trainables(x)
+    end
+end
+
+
+function _trainables(x)
+    arrays = AbstractArray[]
+    fmap(x; exclude = isnumeric, walk = TrainableStructWalk()) do y
+        push!(arrays, y)
+        return y
+    end
+    return arrays
+end
+
+function ∇trainables(x, Δ)
+    i = 0
+    return fmapstructure(x; exclude = isnumeric, walk = TrainableStructWalk()) do _
+                return Δ[i+=1]
+           end
+end
+
+function ChainRulesCore.rrule(::typeof(_trainables), x)
+    y = trainables(x)
+    trainables_back(Δ) = (NoTangent(), ∇trainables(x, unthunk(Δ)))
+    return y, trainables_back
+end
+
+function _trainables_with_path(x)
+    named_params = []
+    exclude(kp, x) = isnumeric(x)
+    fmap_with_path(x; exclude, walk = TrainableStructWalkWithPath()) do kp, y
+        push!(named_params, (kp, y))
+        return y
+    end
+    return named_params
+end
+
+struct TrainableStructWalkWithPath <: AbstractWalk end
+
+function (::TrainableStructWalkWithPath)(recurse, kp::KeyPath, x)
+    x_children = trainable(x)
+    kps = mapkey(c -> KeyPath(kp, c), x_children)
+    return mapvalue(recurse, kps, x_children)
+end
+
+function ChainRulesCore.rrule(::typeof(_trainables_with_path), x)
+    y = _trainables_with_path(x)
+    trainables_with_path_back(Δ) = (NoTangent(), ∇trainables_with_path(x, unthunk(Δ)))
+    return y, trainables_with_path_back
+end
+
+function ∇trainables_with_path(x, Δ)
+    i = 0
+    return fmapstructure(x; exclude = isnumeric, walk = TrainableStructWalk()) do _
+                Δi = Δ[i+=1]
+                if isnothing(Δi)
+                    return nothing
+                else
+                    return Δi[2]
+                end
+           end
+end
diff --git a/src/utils.jl b/src/utils.jl
new file mode 100644
index 00000000..7c6c95be
--- /dev/null
+++ b/src/utils.jl
@@ -0,0 +1,15 @@
+
+mapvalue(f, x...) = map(f, x...)
+mapvalue(f, x::Dict, ys...) = Dict(k => f(v, (get(y, k, nothing) for y in ys)...) for (k,v) in x)
+
+mapkey(f, x::NamedTuple{Ks}) where Ks = NamedTuple{Ks}(map(f, Ks))
+mapkey(f, x::Dict) = Dict(k => f(k) for k in keys(x))
+mapkey(f, x::Tuple) = ntuple(i -> f(i), length(x))
+mapkey(f, x::AbstractArray) = [f(i) for i=1:length(x)]
+
+foreachvalue(f, x...) = foreach(f, x...)
+
+foreachvalue(f, x::Dict, ys...) = foreach(pairs(x)) do (k, v)
+  f(v, (get(y, k, nothing) for y in ys)...)
+end
+
diff --git a/test/runtests.jl b/test/runtests.jl
index e4a14016..fc0fe57f 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -10,7 +10,7 @@ Random.seed!(1)
 
 struct Foo; x; y; end
 Functors.@functor Foo
-Optimisers.trainable(x::Foo) = (x.y, x.x)
+Optimisers.trainable(x::Foo) = (; x.y, x.x)
 
 struct TwoThirds a; b; c; end
 Functors.@functor TwoThirds (a, c)
@@ -539,6 +539,9 @@ end
   @testset verbose=true "Destructure" begin
     include("destructure.jl")
   end
+  @testset verbose=true "Trainables" begin
+    include("trainables.jl")
+  end
   @testset verbose=true "Optimisation Rules" begin
     include("rules.jl")
   end
diff --git a/test/trainables.jl b/test/trainables.jl
new file mode 100644
index 00000000..e1aa0115
--- /dev/null
+++ b/test/trainables.jl
@@ -0,0 +1,141 @@
+
+m1 = collect(1:3.0)
+m2 = (collect(1:3.0), collect(4:6.0))
+m3 = (x = m1, y = sin, z = collect(4:6.0))
+
+m4 = (x = m1, y = m1, z = collect(4:6.0))  # tied
+m5 = (a = (m3, true), b = (m1, false), c = (m4, true))
+m6 = (a = m1, b = [4.0 + im], c = m1)
+
+m7 = TwoThirds((sin, collect(1:3.0)), (cos, collect(4:6.0)), (tan, collect(7:9.0)))
+m8 = [Foo(m1, m1), (a = true, b = Foo([4.0], false), c = ()), [[5.0]]]
+
+mat = Float32[4 6; 5 7]
+m9 = (a = m1, b = mat, c = [mat, m1])
+
+@testset "trainables" begin
+    ps = trainables(m1)
+    @test ps isa Vector
+    @test length(ps) == 1
+    @test ps[1] == m1
+
+    ps = trainables(m2)
+    @test ps isa Vector
+    @test length(ps) == 2
+    @test ps[1] == m2[1]
+    @test ps[2] == m2[2]
+
+    ps = trainables(m3)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == 4:6
+
+    ps = trainables(m4)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == 4:6
+    
+    ps = trainables(m5)
+    @test length(ps) == 3
+    @test ps[1] == 1:3
+    @test ps[2] == 4:6
+    @test ps[3] == 4:6
+
+    ps = trainables(m6)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == ComplexF64[4.0 + 1.0im]
+
+    ps = trainables(m7)
+    @test length(ps) == 1
+    @test ps[1] == [1.0, 2.0, 3.0]
+
+    ps = trainables(m8)
+    @test length(ps) == 3
+    @test ps[1] == 1:3
+    @test ps[2] == [4.0]
+    @test ps[3] == [5.0]
+
+    ps = trainables(m9)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == mat
+end
+
+@testset "gradient" begin
+    loss(m) = sum([sum(abs2, p) for p in trainables(m)])
+    g = gradient(loss, m1)[1]
+    @test g == [2.0, 4.0, 6.0]
+
+    g = gradient(loss, m2)[1]
+    @test g == ([2.0, 4.0, 6.0], [8.0, 10.0, 12.0])
+
+    g = gradient(loss, m3)[1]
+    @test g.x == [2.0, 4.0, 6.0]
+    @test g.y === nothing
+    @test g.z == [8.0, 10.0, 12.0]
+
+    g = gradient(loss, m4)[1]
+    @test g == (x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0], z = [8.0, 10.0, 12.0])
+    g.x === g.y # shared gradient for shared weights
+
+    g = gradient(loss, m5)[1]
+    @test g == (a = ((x = [2.0, 4.0, 6.0], y = nothing, z = [8.0, 10.0, 12.0]), nothing), b = ([2.0, 4.0, 6.0], nothing), c = ((x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0], z = [8.0, 10.0, 12.0]), nothing))
+    
+    g = gradient(loss, m6)[1]
+    @test g == (a = [2.0, 4.0, 6.0], b = ComplexF64[8.0 + 2.0im], c = [2.0, 4.0, 6.0])
+    
+    g = gradient(loss, m7)[1]
+    @test g == (a = (nothing, [2.0, 4.0, 6.0]), b = nothing, c = nothing)
+
+    g = gradient(loss, m8)[1]
+    @test g[1] == (x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0])
+    @test g[2] == (a = nothing, b = (x = [8.0], y = nothing), c = nothing)
+    @test g[3] == [[10.0]]
+
+    g = gradient(loss, m9)[1]
+    @test g == (a = [2.0, 4.0, 6.0], b = Float32[8.0 12.0; 10.0 14.0], c = Array[Float32[8.0 12.0; 10.0 14.0], [2.0, 4.0, 6.0]])
+end
+
+@testset "dict" begin
+    d = Dict(:a => rand(2), :b => ones(2))
+    ps = trainables(d)
+    @test length(ps) == 2
+    @test ps[1] == d[:a]
+    @test ps[2] == d[:b]
+
+    g = gradient(d -> sum(trainables(d)[1].^2) /2 + sum(trainables(d)[2]), d)[1]
+    @test g[:a] == d[:a]
+    @test_broken g[:b] == [1.0, 1.0]
+end
+
+@testset "second order derivatives" begin
+    struct DenseLayer
+        w
+        b
+    end
+
+    Functors.@functor DenseLayer
+
+    loss(m) = sum([sum(abs2, p) for p in trainables(m)])
+
+    model = DenseLayer([1. 2.; 3. 4.], [0., 0.])
+
+    g = gradient(m -> loss(gradient(loss, m)), model)[1]
+    @test g.w == [8.0 16.0; 24.0 32.0]
+    @test g.b == [0.0, 0.0]
+end
+
+@testset "trainables(x, path=true)" begin
+    loss(m) = sum(abs2, trainables(m, path=true)[1][2])
+
+    ps = trainables(m4, path=true)
+    @test length(ps) == 2
+    @test ps[1] == (KeyPath(:x,), [1.0, 2.0, 3.0])
+    @test ps[2] == (KeyPath(:z,), [4.0, 5.0, 6.0])
+
+    g = gradient(loss, m4)[1]
+    @test g.x == [2.0, 4.0, 6.0]
+    @test g.y == [2.0, 4.0, 6.0]
+    @test g.z === nothing
+end