diff --git a/Project.toml b/Project.toml
index b8526d216..dab6288db 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,6 +9,7 @@ IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RealDot = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
diff --git a/src/ChainRules.jl b/src/ChainRules.jl
index 1b5eba024..66dda0909 100644
--- a/src/ChainRules.jl
+++ b/src/ChainRules.jl
@@ -8,6 +8,7 @@ using LinearAlgebra
 using LinearAlgebra.BLAS
 using Random
 using RealDot: realdot
+using SparseArrays
 using Statistics
 
 # Basically everything this package does is overloading these, so we make an exception
@@ -43,6 +44,8 @@ include("rulesets/LinearAlgebra/symmetric.jl")
 include("rulesets/LinearAlgebra/factorization.jl")
 include("rulesets/LinearAlgebra/uniformscaling.jl")
 
+include("rulesets/SparseArrays/sparsematrix.jl")
+
 include("rulesets/Random/random.jl")
 
 end # module
diff --git a/src/rulesets/SparseArrays/sparsematrix.jl b/src/rulesets/SparseArrays/sparsematrix.jl
new file mode 100644
index 000000000..22a5d0366
--- /dev/null
+++ b/src/rulesets/SparseArrays/sparsematrix.jl
@@ -0,0 +1,25 @@
+function rrule(::typeof(sparse), I::AbstractVector, J::AbstractVector, V::AbstractVector, m, n, combine::typeof(+))
+    project_V = ProjectTo(V)
+    
+    function sparse_pullback(Ω̄)
+        ΔΩ = unthunk(Ω̄)
+        ΔV = project_V(ΔΩ[I .+ m .* (J .- 1)])
+        return NoTangent(), NoTangent(), NoTangent(), ΔV, NoTangent(), NoTangent(), NoTangent()
+    end
+
+    return sparse(I, J, V, m, n, combine), sparse_pullback
+end
+
+function rrule(::Type{T}, A::AbstractMatrix) where T <: SparseMatrixCSC
+    function sparse_pullback(Ω̄)
+        return NoTangent(), Ω̄
+    end
+    return T(A), sparse_pullback
+end
+
+function rrule(::Type{T}, v::AbstractVector) where T <: SparseVector
+    function sparse_pullback(Ω̄)
+        return NoTangent(), Ω̄
+    end
+    return T(v), sparse_pullback
+end
diff --git a/test/rulesets/SparseArrays/sparsematrix.jl b/test/rulesets/SparseArrays/sparsematrix.jl
new file mode 100644
index 000000000..3e239cb1c
--- /dev/null
+++ b/test/rulesets/SparseArrays/sparsematrix.jl
@@ -0,0 +1,19 @@
+
+@testset "sparse(I, J, V, m, n, +)" begin
+    m, n = 3, 5
+    s, t, w = [1,2], [2,3], [0.5,0.5]
+    
+    test_rrule(sparse, s, t, w, m, n, +)
+end
+
+@testset "SparseMatrixCSC(A)" begin
+    A = rand(5, 3)
+    test_rrule(SparseMatrixCSC, A)
+    test_rrule(SparseMatrixCSC{Float32,Int}, A, rtol=1e-5)
+end
+
+@testset "SparseVector(v)" begin
+    v = rand(5)
+    test_rrule(SparseVector, v)
+    test_rrule(SparseVector{Float32}, Float32.(v), rtol=1e-5)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 201cb406f..24c1d85b9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -12,6 +12,7 @@ using LinearAlgebra
 using LinearAlgebra.BLAS
 using LinearAlgebra: dot
 using Random
+using SparseArrays
 using StaticArrays
 using Statistics
 using Test
@@ -75,6 +76,10 @@ end
 
     println()
 
+    include_test("rulesets/SparseArrays/sparsematrix.jl")
+
+    println()
+
     include_test("rulesets/Random/random.jl")
     println()
 end