diff --git a/src/host/abstractarray.jl b/src/host/abstractarray.jl
index 440fa836..d0588e80 100644
--- a/src/host/abstractarray.jl
+++ b/src/host/abstractarray.jl
@@ -55,6 +55,8 @@ Base._show_empty(io::IO, X::AnyGPUArray) =
     Base._show_empty(io, adapt(ToArray(), X))
 Base.show_vector(io::IO, v::AnyGPUArray, args...) =
     Base.show_vector(io, adapt(ToArray(), v), args...)
+Base.show_zero_dim(io::IO, X::AnyGPUArray{T, 0}) where T =
+    Base.show_zero_dim(io, adapt(ToArray(), X))
 
 ## collect to CPU (discarding wrapper type)
 
diff --git a/src/host/mapreduce.jl b/src/host/mapreduce.jl
index cb5b489e..fd1ff205 100644
--- a/src/host/mapreduce.jl
+++ b/src/host/mapreduce.jl
@@ -90,4 +90,7 @@ for (fname, op) in [(:sum, :(Base.add_sum)), (:prod, :(Base.mul_prod)),
     end
 end
 
+Base._mapreduce_dim(f, op, init, A::AnyGPUArray{<:Any,0}, ::Colon) = op(f(@allowscalar A[]), init)
+Base._mapreduce_dim(f, op, ::Base._InitialValue, A::AnyGPUArray{<:Any,0}, ::Colon) = f(@allowscalar A[])
+
 LinearAlgebra.ishermitian(A::AbstractGPUMatrix) = mapreduce(==, &, A, adjoint(A))
diff --git a/test/testsuite/io.jl b/test/testsuite/io.jl
index 7d0c58e4..27811f1b 100644
--- a/test/testsuite/io.jl
+++ b/test/testsuite/io.jl
@@ -30,5 +30,13 @@
         @test occursin(Regex("^1×1 Adjoint{Int64,\\s?$AT{Int64,\\s?1}}:\n 1\$"), msg) ||
             occursin(Regex("^1×1 LinearAlgebra.Adjoint{Int64,\\s?$AT{Int64,\\s?1}}:\n 1\$"), msg) ||
             occursin(Regex("^1×1 adjoint\\(::$AT{Int64,\\s?1}\\) with eltype Int64:\n 1\$"), msg)
+
+        C = AT(fill(1))
+        msg = showstr(A)
+        if VERSION >= v"1.7-"
+            @test msg == "fill(1)"
+        else
+            @test msg == "[1]"
+        end
     end
 end
diff --git a/test/testsuite/reductions.jl b/test/testsuite/reductions.jl
index a07ce04e..510085f8 100644
--- a/test/testsuite/reductions.jl
+++ b/test/testsuite/reductions.jl
@@ -140,3 +140,22 @@ end
         @test A != B
     end
 end
+
+@testsuite "reductions/zero-arrays" AT->begin
+    @testset "$ET" for ET in supported_eltypes()
+        range = ET <: Real ? (ET(1):ET(10)) : ET
+        # sum
+        @test compare(A->sum(A), AT, reshape(rand(range, 1)))
+        @test compare(A->sum(abs, A), AT, reshape(rand(range, 1)))
+        if VERSION >= v"1.6"
+            @test compare(A->sum(A, init=ET(13)), AT, reshape(rand(range, 1)))
+        end
+        # other functions, defined together
+        @test compare(A->prod(A), AT, reshape(rand(range, 1)))
+        @test compare(A->any(_->true, A), AT, reshape(rand(range, 1)))
+        @test compare(A->all(_->false, A), AT, reshape(rand(range, 1)))
+        # zero-dimensional view
+        @test compare(A->sum(A), AT, view(rand(range, 3),2))
+        @test compare(A->prod(sqrt, A), AT, view(rand(range, 3),2))
+    end
+end