diff --git a/Project.toml b/Project.toml
index 2f70bb7ac..7b8b7204b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -8,6 +8,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
diff --git a/src/ChainRules.jl b/src/ChainRules.jl
index d7e0082d0..1c94580e7 100644
--- a/src/ChainRules.jl
+++ b/src/ChainRules.jl
@@ -9,6 +9,7 @@ using LinearAlgebra.BLAS
 using Random
 using Requires
 using Statistics
+using SparseArrays
 
 # Basically everything this package does is overloading these, so we make an exception
 # to the normal rule of only overload via `ChainRulesCore.rrule`.
@@ -37,6 +38,8 @@ include("rulesets/LinearAlgebra/dense.jl")
 include("rulesets/LinearAlgebra/structured.jl")
 include("rulesets/LinearAlgebra/factorization.jl")
 
+include("rulesets/SparseArrays/sparsematrix.jl")
+
 include("rulesets/Random/random.jl")
 
 # Note: The following is only required because package authors sometimes do not
diff --git a/src/rulesets/LinearAlgebra/dense.jl b/src/rulesets/LinearAlgebra/dense.jl
index 9800363c1..5affa37e1 100644
--- a/src/rulesets/LinearAlgebra/dense.jl
+++ b/src/rulesets/LinearAlgebra/dense.jl
@@ -332,3 +332,13 @@ function rrule(::typeof(norm), x::Real, p::Real=2)
     end
     return norm(x, p), norm_pullback
 end
+
+function rrule(::typeof(diagm), x::AbstractVector)
+    diagm_pullback(∂x) = (NO_FIELDS, diag(∂x),)
+    return diagm(x), diagm_pullback
+end
+
+function rrule(::typeof(issymmetric), x)
+    issymmetric_pullback(∂x) = (NO_FIELDS, ∂x)
+    return issymmetric(x), issymmetric_pullback
+end
diff --git a/src/rulesets/SparseArrays/sparsematrix.jl b/src/rulesets/SparseArrays/sparsematrix.jl
new file mode 100644
index 000000000..eb002ecfe
--- /dev/null
+++ b/src/rulesets/SparseArrays/sparsematrix.jl
@@ -0,0 +1,15 @@
+using SparseArrays
+
+function rrule(::Type{<:SparseMatrixCSC{T,N}}, arr) where {T,N}
+    function SparseMatrix_pullback(Δ)
+        return NO_FIELDS, collect(Δ)
+    end
+    return SparseMatrixCSC{T,N}(arr), SparseMatrix_pullback
+end
+
+function rrule(::typeof(Matrix), x::SparseMatrixCSC)
+  function Matrix_pullback(Δ)
+      NO_FIELDS, Δ
+  end
+  return Matrix(x), Matrix_pullback
+end
diff --git a/test/rulesets/SparseArrays/sparsematrix.jl b/test/rulesets/SparseArrays/sparsematrix.jl
new file mode 100644
index 000000000..52161a511
--- /dev/null
+++ b/test/rulesets/SparseArrays/sparsematrix.jl
@@ -0,0 +1,8 @@
+using SparseArrays
+
+@testset "Sparse" begin
+    r = sparse(rand(3,3))
+    x, x̄ = rand(3,3), rand(3,3)
+    test_rrule(SparseMatrixCSC, r)
+    test_rrule(Matrix, r)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 740d87bca..0bffb7ef9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -10,6 +10,7 @@ using LinearAlgebra.BLAS
 using LinearAlgebra: dot
 using Random
 using Statistics
+using SparseArrays
 using Test
 
 Random.seed!(1) # Set seed that all testsets should reset to.
@@ -48,6 +49,12 @@ println("Testing ChainRules.jl")
 
         print(" ")
 
+        @testset "SparseArrays" begin
+            include(joinpath("rulesets", "SparseArrays", "sparsematrix.jl"))
+        end
+
+        print(" ")
+
         @testset "packages" begin
             include(joinpath("rulesets", "packages", "NaNMath.jl"))
             include(joinpath("rulesets", "packages", "SpecialFunctions.jl"))