diff --git a/docs/src/models/layers.md b/docs/src/models/layers.md
index d92388e1..cb0c6615 100644
--- a/docs/src/models/layers.md
+++ b/docs/src/models/layers.md
@@ -5,6 +5,7 @@ These core layers form the foundation of almost all neural networks.
 ```@docs
 Chain
 Dense
+Conv2D
 ```
 
 ## Recurrent Layers
diff --git a/src/Flux.jl b/src/Flux.jl
index 526d6bb8..2acdb177 100644
--- a/src/Flux.jl
+++ b/src/Flux.jl
@@ -7,13 +7,14 @@ module Flux
 using Juno, Requires
 using Lazy: @forward
 
-export Chain, Dense, RNN, LSTM,
+export Chain, Dense, RNN, LSTM, Conv2D,
   Dropout, LayerNorm, BatchNorm,
   SGD, ADAM, Momentum, Nesterov, AMSGrad,
   param, params, mapleaves
 
 using NNlib
-export σ, sigmoid, relu, leakyrelu, elu, swish, softmax
+export σ, sigmoid, relu, leakyrelu, elu, swish, softmax,
+  conv2d, maxpool2d, avgpool2d
 
 include("tracker/Tracker.jl")
 using .Tracker
@@ -27,6 +28,7 @@ include("treelike.jl")
 
 include("layers/stateless.jl")
 include("layers/basic.jl")
+include("layers/conv.jl")
 include("layers/recurrent.jl")
 include("layers/normalisation.jl")
 
diff --git a/src/layers/conv.jl b/src/layers/conv.jl
new file mode 100644
index 00000000..e267510b
--- /dev/null
+++ b/src/layers/conv.jl
@@ -0,0 +1,33 @@
+"""
+    Conv2D(size, in=>out)
+    Conv2d(size, in=>out, relu)
+
+Standard convolutional layer. `size` should be a tuple like `(2, 2)`.
+`in` and `out` specify the number of input and output channels respectively.
+
+Data should be stored in HWCN order. In other words, a 100×100 RGB image would
+be a `100×100×3` array, and a batch of 50 would be a `100×100×3×50` array.
+
+Takes the keyword arguments `pad` and `stride`.
+"""
+struct Conv2D{F,A}
+  σ::F
+  weight::A
+  stride::Int
+  pad::Int
+end
+
+Conv2D(k::NTuple{2,Integer}, ch::Pair{<:Integer,<:Integer}, σ = identity;
+       init = initn, stride = 1, pad = 0) =
+  Conv2D(σ, param(initn(k..., ch...)), stride, pad)
+
+Flux.treelike(Conv2D)
+
+(c::Conv2D)(x) = c.σ.(conv2d(x, c.weight, stride = c.stride, padding = c.pad))
+
+function Base.show(io::IO, l::Conv2D)
+  print(io, "Conv2D((", size(l.weight, 1), ", ", size(l.weight, 2), ")")
+  print(io, ", ", size(l.weight, 3), "=>", size(l.weight, 4))
+  l.σ == identity || print(io, ", ", l.σ)
+  print(io, ")")
+end
diff --git a/src/onehot.jl b/src/onehot.jl
index f94fb93e..4f121958 100644
--- a/src/onehot.jl
+++ b/src/onehot.jl
@@ -18,7 +18,9 @@ end
 
 Base.size(xs::OneHotMatrix) = (Int64(xs.height),length(xs.data))
 
-Base.getindex(xs::OneHotMatrix, i::Int, j::Int) = xs.data[j][i]
+Base.getindex(xs::OneHotMatrix, i::Integer, j::Integer) = xs.data[j][i]
+Base.getindex(xs::OneHotMatrix, ::Colon, i::Integer) = xs.data[i]
+Base.getindex(xs::OneHotMatrix, ::Colon, i::AbstractArray) = OneHotMatrix(xs.height, xs.data[i])
 
 A::AbstractMatrix * B::OneHotMatrix = A[:, map(x->x.ix, B.data)]
 
diff --git a/src/tracker/back.jl b/src/tracker/back.jl
index 39810069..b4cd27c6 100644
--- a/src/tracker/back.jl
+++ b/src/tracker/back.jl
@@ -12,16 +12,17 @@ function scan(x::TrackedArray)
   return
 end
 
-back(c::Call, Δ) = back(c.func, Δ, c.args...)
-back(::Call{Void}, Δ) = nothing
+back_(f, y, args...) = back(f, args...)
+back_(c::Call, y, Δ) = back_(c.func, y, Δ, c.args...)
+back_(::Call{Void}, y, Δ) = nothing
 
 function back(x::TrackedArray, Δ)
   ref = x.ref -= 1
   if isdefined(x, :grad)
     x.grad .+= Δ
-    ref == 0 && back(x.f, x.grad)
+    ref == 0 && back_(x.f, x.data, x.grad)
   else
-    ref == 0 && back(x.f, Δ)
+    ref == 0 && back_(x.f, x.data, Δ)
   end
   return
 end
@@ -35,6 +36,9 @@ end
 
 # Interface methods
 
+# TODO: if an error occurs in `back` the refcounts will be broken
+# and `back` will silently fail to update.
+
 function back!(x::TrackedArray, Δ)
   scan(x)
   back(x, Δ)
diff --git a/src/tracker/lib.jl b/src/tracker/lib.jl
index f3221bd8..2dc25e52 100644
--- a/src/tracker/lib.jl
+++ b/src/tracker/lib.jl
@@ -44,6 +44,12 @@ function back(::typeof(vcat), Δ, xs, ys)
   @back(ys, Δ[size(xs,1)+1:end, i...])
 end
 
+Base.reshape(xs::TrackedArray, dims::Union{Colon,Int64}...) =
+  TrackedArray(Call(reshape, xs, dims...))
+
+back(::typeof(reshape), Δ, xs::TrackedArray, _...) =
+  back(xs, reshape(Δ, size(xs)))
+
 # Reductions
 
 Base.sum(xs::TrackedArray, dim) = TrackedArray(Call(sum, xs, dim))
@@ -123,12 +129,36 @@ end
 
 # NNlib
 
-import NNlib: softmax, ∇softmax
+using NNlib
+import NNlib: softmax, ∇softmax, conv2d, pool
 
 softmax(xs::TrackedArray) = TrackedArray(Call(softmax, xs))
 
 back(::typeof(softmax), Δ, xs) = @back(xs, ∇softmax(Δ, data(xs)))
 
+# TODO: can store kwargs efficiently in namedtuples
+_conv2d(x, w, stride, pad) = conv2d(x, w, stride = stride, padding = pad)
+
+conv2d(x::TrackedArray{<:Any,4}, w::TrackedArray{<:Any,4}; stride = 1, padding = 0) =
+  TrackedArray(Call(_conv2d, x, w, stride, padding))
+conv2d(x::AbstractArray{<:Any,4}, w::TrackedArray{<:Any,4}; stride = 1, padding = 0) =
+  TrackedArray(Call(_conv2d, x, w, stride, padding))
+conv2d(x::TrackedArray{<:Any,4}, w::AbstractArray{<:Any,4}; stride = 1, padding = 0) =
+  TrackedArray(Call(_conv2d, x, w, stride, padding))
+
+function back(::typeof(_conv2d), Δ, x, w, stride, pad)
+  @back(x, NNlib.conv2d_grad_x(data(x), data(w), Δ; stride = stride, padding = pad))
+  @back(w, NNlib.conv2d_grad_w(data(x), data(w), Δ; stride = stride, padding = pad))
+end
+
+_pool(x, k, mode) = pool(x, window = k, mode = mode)
+
+pool(x::TrackedArray{<:Any,4}; window = 2, mode = 0) =
+  TrackedArray(Call(_pool, x, window, mode))
+
+back_(::typeof(_pool), y, Δ, x, k, mode) =
+  back(x, NNlib.pool_grad(data(x), y, Δ, window = k, mode = mode))
+
 # Broadcasting
 
 using ForwardDiff: Dual, partials
diff --git a/src/tracker/numeric.jl b/src/tracker/numeric.jl
index 68211aa3..cbcd3ad8 100644
--- a/src/tracker/numeric.jl
+++ b/src/tracker/numeric.jl
@@ -19,4 +19,4 @@ function ngradient(f, xs::AbstractArray...)
   return grads
 end
 
-gradcheck(f, xs...) = all(isapprox.(ngradient(f, xs...), gradient(f, xs...), rtol = 1e-6))
+gradcheck(f, xs...) = all(isapprox.(ngradient(f, xs...), gradient(f, xs...), rtol = 1e-5))
diff --git a/src/utils.jl b/src/utils.jl
index afe926d9..bba3e416 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -4,8 +4,6 @@ initn(dims...) = randn(dims...)/100
 glorot_uniform(dims...) = (rand(dims...) - 0.5)*sqrt(24.0/(sum(dims)))
 glorot_normal(dims...) = (randn(dims...)*sqrt(2.0/sum(dims)))
 
-flatten(xs) = reshape(xs, size(xs, 1), :)
-
 unsqueeze(xs, dim) = reshape(xs, (size(xs)[1:dim-1]..., 1, size(xs)[dim:end]...))
 
 stack(xs, dim) = cat(dim, unsqueeze.(xs, dim)...)
diff --git a/test/tracker.jl b/test/tracker.jl
index ac031915..dc11420b 100644
--- a/test/tracker.jl
+++ b/test/tracker.jl
@@ -1,5 +1,6 @@
 using Flux.Tracker, Base.Test, NNlib
 using Flux.Tracker: gradcheck
+using NNlib
 
 gradtest(f, xs::AbstractArray...) = gradcheck((xs...) -> sum(f(xs...)), xs...)
 gradtest(f, dims...) = gradtest(f, rand.(dims)...)
@@ -45,4 +46,8 @@ end
   2y + x
 end
 
+@test gradtest(conv2d, rand(10, 10, 3, 2), randn(2, 2, 3, 2))
+@test gradtest(x -> maxpool2d(x, 2), rand(10, 10, 3, 2))
+@test gradtest(x -> avgpool2d(x, 2), rand(10, 10, 3, 2))
+
 end #testset