diff --git a/Project.toml b/Project.toml
index a3b2c3d26..bd8155f02 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesCore"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.8.0"
+version = "1.9.0"
 
 [deps]
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
diff --git a/src/projection.jl b/src/projection.jl
index c4bbf4575..e5542d4d8 100644
--- a/src/projection.jl
+++ b/src/projection.jl
@@ -272,18 +272,55 @@ end
 #####
 
 # Ref
+# Note that Ref is mutable. This causes Zygote to represent its structral tangent not as a NamedTuple,
+# but as `Ref{Any}((x=val,))`. Here we use a Tangent, there is at present no mutable version, but see
+# https://github.com/JuliaDiff/ChainRulesCore.jl/issues/105
 function ProjectTo(x::Ref)
     sub = ProjectTo(x[])  # should we worry about isdefined(Ref{Vector{Int}}(), :x)? 
-    if sub isa ProjectTo{<:AbstractZero}
+    return ProjectTo{Tangent{typeof(x)}}(; x=sub)
+end
+(project::ProjectTo{<:Tangent{<:Ref}})(dx::Tangent) = project(Ref(first(backing(dx))))
+function (project::ProjectTo{<:Tangent{<:Ref}})(dx::Ref)
+    dy = project.x(dx[])
+    return project_type(project)(; x=dy)
+end
+# Since this works like a zero-array in broadcasting, it should also accept a number:
+(project::ProjectTo{<:Tangent{<:Ref}})(dx::Number) = project(Ref(dx))
+
+# Tuple
+function ProjectTo(x::Tuple)
+    elements = map(ProjectTo, x)
+    if elements isa NTuple{<:Any,ProjectTo{<:AbstractZero}}
         return ProjectTo{NoTangent}()
     else
-        return ProjectTo{Ref}(; type=typeof(x), x=sub)
+        return ProjectTo{Tangent{typeof(x)}}(; elements=elements)
     end
 end
-(project::ProjectTo{Ref})(dx::Tangent{<:Ref}) = Tangent{project.type}(; x=project.x(dx.x))
-(project::ProjectTo{Ref})(dx::Ref) = Tangent{project.type}(; x=project.x(dx[]))
-# Since this works like a zero-array in broadcasting, it should also accept a number:
-(project::ProjectTo{Ref})(dx::Number) = Tangent{project.type}(; x=project.x(dx))
+# This method means that projection is re-applied to the contents of a Tangent.
+# We're not entirely sure whether this is every necessary; but it should be safe,
+# and should often compile away:
+(project::ProjectTo{<:Tangent{<:Tuple}})(dx::Tangent) = project(backing(dx))
+function (project::ProjectTo{<:Tangent{<:Tuple}})(dx::Tuple)
+    len = length(project.elements)
+    if length(dx) != len
+        str = "tuple with length(x) == $len cannot have a gradient with length(dx) == $(length(dx))"
+        throw(DimensionMismatch(str))
+    end
+    # Here map will fail if the lengths don't match, but gives a much less helpful error:
+    dy = map((f, x) -> f(x), project.elements, dx)
+    return project_type(project)(dy...)
+end
+function (project::ProjectTo{<:Tangent{<:Tuple}})(dx::AbstractArray)
+    for d in 1:ndims(dx)
+        if size(dx, d) != get(length(project.elements), d, 1)
+            throw(_projection_mismatch(axes(project.elements), size(dx)))
+        end
+    end
+    dy = reshape(dx, axes(project.elements))  # allows for dx::OffsetArray
+    dz = ntuple(i -> project.elements[i](dy[i]), length(project.elements))
+    return project_type(project)(dz...)
+end
+
 
 #####
 ##### `LinearAlgebra`
diff --git a/test/projection.jl b/test/projection.jl
index d0c6c7eca..592b0a84d 100644
--- a/test/projection.jl
+++ b/test/projection.jl
@@ -137,12 +137,29 @@ struct NoSuperType end
         prefvec = ProjectTo(Ref([1, 2, 3 + 4im]))  # recurses into contents
         @test prefvec(Ref(1:3)).x isa Vector{ComplexF64}
         @test prefvec(Tangent{Base.RefValue}(; x=1:3)).x isa Vector{ComplexF64}
-        @test_skip @test_throws DimensionMismatch prefvec(Tangent{Base.RefValue}(; x=1:5))
+        @test_throws DimensionMismatch prefvec(Tangent{Base.RefValue}(; x=1:5))
 
         @test ProjectTo(Ref(true)) isa ProjectTo{NoTangent}
         @test ProjectTo(Ref([false]')) isa ProjectTo{NoTangent}
     end
 
+    @testset "Base: Tuple" begin
+        pt1 = ProjectTo((1.0,))
+        @test pt1((1 + im,)) == Tangent{Tuple{Float64}}(1.0,)
+        @test pt1(pt1((1,))) == pt1(pt1((1,)))            # accepts correct Tangent
+        @test pt1(Tangent{Any}(1)) == pt1((1,))           # accepts Tangent{Any}
+        @test pt1([1,]) == Tangent{Tuple{Float64}}(1.0,)  # accepts Vector
+        @test pt1(NoTangent()) === NoTangent()
+        @test pt1(ZeroTangent()) === ZeroTangent()
+
+        @test_throws Exception pt1([1, 2]) # DimensionMismatch, wrong length
+        @test_throws Exception pt1([])
+
+        pt3 = ProjectTo(([1, 2, 3], false, :gamma)) # partly non-differentiable
+        @test pt3((1:3, 4, 5)) == Tangent{Tuple{Vector{Int}, Bool, Symbol}}([1.0, 2.0, 3.0], NoTangent(), NoTangent())
+        @test ProjectTo((true, [false])) isa ProjectTo{NoTangent}
+    end
+
     @testset "Base: non-diff" begin
         @test ProjectTo(:a)(1) == NoTangent()
         @test ProjectTo('b')(2) == NoTangent()