diff --git a/base/missing.jl b/base/missing.jl
index dd829995d98cd..fd99729e78b93 100644
--- a/base/missing.jl
+++ b/base/missing.jl
@@ -146,6 +146,9 @@ float(A::AbstractArray{Missing}) = A
     skipmissing(itr)
 
 Return an iterator over the elements in `itr` skipping [`missing`](@ref) values.
+In addition to supporting any function taking iterators, the resulting object
+implements reductions over dimensions (i.e. the `dims` argument to
+[`mapreduce`](@ref), [`reduce`](@ref) and special functions like [`sum`](@ref)).
 
 Use [`collect`](@ref) to obtain an `Array` containing the non-`missing` values in
 `itr`. Note that even if `itr` is a multidimensional array, the result will always
@@ -154,9 +157,6 @@ of the input.
 
 # Examples
 ```jldoctest
-julia> sum(skipmissing([1, missing, 2]))
-3
-
 julia> collect(skipmissing([1, missing, 2]))
 2-element Array{Int64,1}:
  1
@@ -166,6 +166,31 @@ julia> collect(skipmissing([1 missing; 2 missing]))
 2-element Array{Int64,1}:
  1
  2
+
+julia> sum(skipmissing([1, missing, 2]))
+3
+
+julia> B = [1 missing; 3 4]
+2×2 Array{Union{Missing, Int64},2}:
+ 1   missing
+ 3  4
+
+julia> sum(skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 4  4
+
+julia> sum(skipmissing(B), dims=2)
+2×1 Array{Int64,2}:
+ 1
+ 7
+
+julia> reduce(*, skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 3  4
+
+julia> mapreduce(cos, +, skipmissing(B), dims=1)
+1×2 Array{Float64,2}:
+ -0.44969  -0.653644
 ```
 """
 skipmissing(itr) = SkipMissing(itr)
@@ -192,8 +217,8 @@ end
 # Optimized mapreduce implementation
 # The generic method is faster when !(eltype(A) >: Missing) since it does not need
 # additional loops to identify the two first non-missing values of each block
-mapreduce(f, op, itr::SkipMissing{<:AbstractArray}) =
-    _mapreduce(f, op, IndexStyle(itr.x), eltype(itr.x) >: Missing ? itr : itr.x)
+mapreduce(f, op, itr::SkipMissing{<:AbstractArray}; dims=:, kw...) =
+    _mapreduce_dim(f, op, kw.data, eltype(itr.x) >: Missing ? itr : itr.x, dims)
 
 function _mapreduce(f, op, ::IndexLinear, itr::SkipMissing{<:AbstractArray})
     A = itr.x
@@ -280,6 +305,185 @@ mapreduce_impl(f, op, A::SkipMissing, ifirst::Integer, ilast::Integer) =
     end
 end
 
+# mapreduce over dimensions implementation
+
+_mapreduce_dim(f, op, nt::NamedTuple{(:init,)}, itr::SkipMissing{<:AbstractArray}, ::Colon) =
+    mapfoldl(f, op, itr; nt...)
+
+_mapreduce_dim(f, op, ::NamedTuple{()}, itr::SkipMissing{<:AbstractArray}, ::Colon) =
+    _mapreduce(f, op, IndexStyle(itr.x), itr)
+
+_mapreduce_dim(f, op, nt::NamedTuple{(:init,)}, itr::SkipMissing{<:AbstractArray}, dims) =
+    mapreducedim!(f, op, reducedim_initarray(itr, dims, nt.init), itr)
+
+_mapreduce_dim(f, op, ::NamedTuple{()}, itr::SkipMissing{<:AbstractArray}, dims) =
+    mapreducedim!(f, op, reducedim_init(f, op, itr, dims), itr)
+
+reducedim_initarray(itr::SkipMissing{<:AbstractArray}, region, init, ::Type{R}) where {R} =
+    reducedim_initarray(itr.x, region, init, R)
+reducedim_initarray(itr::SkipMissing{<:AbstractArray}, region, init::T) where {T} =
+    reducedim_initarray(itr.x, region, init, T)
+
+reducedim_init(f, op::Union{typeof(+),typeof(add_sum)},
+               itr::SkipMissing{<:AbstractArray}, region) =
+    _reducedim_init(f, op, zero, sum, itr, region)
+reducedim_init(f, op::Union{typeof(*),typeof(mul_prod)},
+               itr::SkipMissing{<:AbstractArray}, region) =
+    _reducedim_init(f, op, one, prod, itr, region)
+reducedim_init(f::Union{typeof(abs),typeof(abs2)}, op::typeof(max),
+               itr::SkipMissing{<:AbstractArray}, region) =
+    reducedim_initarray(itr, region, zero(f(zero(eltype(itr)))))
+reducedim_init(f, op::typeof(&), itr::SkipMissing{<:AbstractArray}, region) =
+    reducedim_initarray(itr, region, true)
+reducedim_init(f, op::typeof(|), itr::SkipMissing{<:AbstractArray}, region) =
+    reducedim_initarray(itr, region, false)
+
+# initialization when computing minima and maxima requires a little care
+for (f1, f2, initval) in ((:min, :max, :Inf), (:max, :min, :(-Inf)))
+    @eval function reducedim_init(f, op::typeof($f1), itr::SkipMissing{<:AbstractArray}, region)
+        A = itr.x
+        T = eltype(itr)
+
+        # First compute the reduce indices. This will throw an ArgumentError
+        # if any region is invalid
+        ri = reduced_indices(A, region)
+
+        # Next, throw if reduction is over a region with length zero
+        any(i -> isempty(axes(A, i)), region) && _empty_reduce_error()
+
+        # Make a view of the first slice of the region
+        A1 = view(A, ri...)
+
+        if isempty(A1)
+            # If the slice is empty just return non-view, non-missing version as the initial array
+            return similar(A1, eltype(itr))
+        else
+            # otherwise use the min/max of the first slice as initial value
+            v0 = mapreduce(f, $f2, A1)
+
+            R = similar(A1, typeof(v0))
+
+            # if any value is missing in first slice, look for first
+            # non-missing value in each slice
+            if v0 === missing
+                v0 = nonmissingval(f, $f2, itr, R)
+                R = similar(A1, typeof(v0))
+            end
+
+            # but NaNs need to be avoided as initial values
+            v0 = v0 != v0 ? typeof(v0)($initval) : v0
+
+            # equivalent to reducedim_initarray, but we need R in advance
+            return fill!(R, v0)
+        end
+    end
+end
+
+# Iterate until we've encountered at least one non-missing value in each slice,
+# and return the min/max non-missing value of all clices
+function nonmissingval(f, op::Union{typeof(min), typeof(max)},
+                       itr::SkipMissing{<:AbstractArray}, R::AbstractArray)
+    A = itr.x
+    lsiz = check_reducedims(R,A)
+    indsAt, indsRt = safe_tail(axes(A)), safe_tail(axes(R)) # handle d=1 manually
+    keep, Idefault = Broadcast.shapeindexer(indsRt)
+    i = findfirst(!ismissing, A)
+    i === nothing && throw(ArgumentError("cannot reduce over array with only missing values"))
+    @inbounds v = A[i]
+    if reducedim1(R, A)
+        # keep track of state using a single variable when reducing along the first dimension
+        i1 = first(axes1(R))
+        @inbounds for IA in CartesianIndices(indsAt)
+            IR = Broadcast.newindex(IA, keep, Idefault)
+            filled = false
+            for i in axes(A, 1)
+                x = A[i, IA]
+                if x !== missing
+                    v = op(v, f(x))
+                    filled = true
+                    break
+                end
+            end
+            if !filled
+                throw(ArgumentError("cannot reduce over slices with only missing values"))
+            end
+        end
+    else
+        filled = fill!(similar(R, Bool), false)
+        allfilled = false
+        @inbounds for IA in CartesianIndices(indsAt)
+            IR = Broadcast.newindex(IA, keep, Idefault)
+            for i in axes(A, 1)
+                x = A[i, IA]
+                if x !== missing
+                    v = op(v, f(x))
+                    filled[i,IR] = true
+                end
+            end
+            (allfilled = all(filled)) && break
+        end
+        if !allfilled
+            throw(ArgumentError("cannot reduce over slices with only missing values"))
+        end
+    end
+    v
+end
+
+function _mapreducedim!(f, op, R::AbstractArray, itr::SkipMissing{<:AbstractArray})
+    A = itr.x
+    lsiz = check_reducedims(R,A)
+    isempty(A) && return R
+
+    if has_fast_linear_indexing(A) && lsiz > 16
+        # use mapreduce_impl, which is probably better tuned to achieve higher performance
+        nslices = div(length(A), lsiz)
+        ibase = first(LinearIndices(A))-1
+        for i = 1:nslices
+            x = mapreduce_impl(f, op, itr, ibase+1, ibase+lsiz)
+            if x !== nothing
+                @inbounds R[i] = op(R[i], something(x))
+            end
+            ibase += lsiz
+        end
+        return R
+    end
+    indsAt, indsRt = safe_tail(axes(A)), safe_tail(axes(R)) # handle d=1 manually
+    keep, Idefault = Broadcast.shapeindexer(indsRt)
+    if reducedim1(R, A)
+        # keep the accumulator as a local variable when reducing along the first dimension
+        i1 = first(axes1(R))
+        @inbounds for IA in CartesianIndices(indsAt)
+            IR = Broadcast.newindex(IA, keep, Idefault)
+            r = R[i1,IR]
+            @simd for i in axes(A, 1)
+                x = A[i, IA]
+                if x !== missing
+                    r = op(r, f(x))
+                end
+            end
+
+            R[i1,IR] = r
+        end
+    else
+        @inbounds for IA in CartesianIndices(indsAt)
+            IR = Broadcast.newindex(IA, keep, Idefault)
+            @simd for i in axes(A, 1)
+                x = A[i, IA]
+                if x !== missing
+                    R[i,IR] = op(R[i,IR], f(x))
+                end
+            end
+        end
+    end
+    return R
+end
+
+mapreducedim!(f, op, R::AbstractArray, A::SkipMissing{<:AbstractArray}) =
+    (_mapreducedim!(f, op, R, A); R)
+
+reducedim!(op, R::AbstractArray{RT}, A::SkipMissing{<:AbstractArray}) where {RT} =
+    mapreducedim!(identity, op, R, A)
+
 """
     coalesce(x, y...)
 
diff --git a/base/reducedim.jl b/base/reducedim.jl
index 150b93c7e8f5a..7a212d7496d46 100644
--- a/base/reducedim.jl
+++ b/base/reducedim.jl
@@ -288,6 +288,15 @@ julia> mapreduce(isodd, *, a, dims=1)
 julia> mapreduce(isodd, |, true, a, dims=1)
 1×4 Array{Bool,2}:
  true  true  true  true
+
+julia> b = [1 missing 5; 2 4 missing]
+2×3 Array{Union{Missing, Int64},2}:
+ 1   missing  5
+ 2  4          missing
+
+julia> mapreduce(isodd, *, skipmissing(b), dims=1)
+1×3 Array{Bool,2}:
+ false  false  true
 ```
 """
 mapreduce(f, op, A::AbstractArray; dims=:, kw...) = _mapreduce_dim(f, op, kw.data, A, dims)
@@ -332,6 +341,15 @@ julia> reduce(max, a, dims=2)
 julia> reduce(max, a, dims=1)
 1×4 Array{Int64,2}:
  4  8  12  16
+
+julia> b = [1 missing 5; 2 4 missing]
+2×3 Array{Union{Missing, Int64},2}:
+ 1   missing  5
+ 2  4          missing
+
+julia> reduce(+, skipmissing(b), dims=1)
+1×3 Array{Int64,2}:
+ 3  4  5
 ```
 """
 reduce(op, A::AbstractArray; kw...) = mapreduce(identity, op, A; kw...)
@@ -342,6 +360,12 @@ reduce(op, A::AbstractArray; kw...) = mapreduce(identity, op, A; kw...)
 
 Sum elements of an array over the given dimensions.
 
+!!! note
+    If `A` contains `NaN` or [`missing`](@ref) values, they are propagated to the
+    corresponding result (`missing` takes precedence if a slice contains both).
+    Use [`skipmissing(A)`](@ref) to omit `missing` entries and compute the
+    sum of non-missing values.
+
 # Examples
 ```jldoctest
 julia> A = [1 2; 3 4]
@@ -357,6 +381,20 @@ julia> sum(A, dims=2)
 2×1 Array{Int64,2}:
  3
  7
+
+julia> B = [1 missing; 3 4]
+2×2 Array{Union{Missing, Int64},2}:
+ 1   missing
+ 3  4
+
+julia> sum(skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 4  4
+
+julia> sum(skipmissing(B), dims=2)
+2×1 Array{Int64,2}:
+ 1
+ 7
 ```
 """
 sum(A::AbstractArray; dims)
@@ -390,6 +428,12 @@ sum!(r, A)
 
 Multiply elements of an array over the given dimensions.
 
+!!! note
+    If `A` contains `NaN` or [`missing`](@ref) values, they are propagated to the
+    corresponding result (`missing` takes precedence if a slice contains both).
+    Use [`skipmissing(A)`](@ref) to omit `missing` entries and compute the
+    product of non-missing values.
+
 # Examples
 ```jldoctest
 julia> A = [1 2; 3 4]
@@ -405,6 +449,20 @@ julia> prod(A, dims=2)
 2×1 Array{Int64,2}:
   2
  12
+
+julia> B = [1 missing; 3 4]
+2×2 Array{Union{Missing, Int64},2}:
+ 1   missing
+ 3  4
+
+julia> prod(skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 3  4
+
+julia> prod(skipmissing(B), dims=2)
+2×1 Array{Int64,2}:
+  1
+ 12
 ```
 """
 prod(A::AbstractArray; dims)
@@ -440,6 +498,12 @@ Compute the maximum value of an array over the given dimensions. See also the
 [`max(a,b)`](@ref) function to take the maximum of two or more arguments,
 which can be applied elementwise to arrays via `max.(a,b)`.
 
+!!! note
+    If `A` contains `NaN` or [`missing`](@ref) values, they are propagated to the
+    corresponding result (`missing` takes precedence if a slice contains both).
+    Use [`skipmissing(A)`](@ref) to omit `missing` entries and compute the
+    maximum of non-missing values.
+
 # Examples
 ```jldoctest
 julia> A = [1 2; 3 4]
@@ -455,6 +519,20 @@ julia> maximum(A, dims=2)
 2×1 Array{Int64,2}:
  2
  4
+
+julia> B = [1 missing; 3 4]
+2×2 Array{Union{Missing, Int64},2}:
+ 1   missing
+ 3  4
+
+julia> maximum(skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 3  4
+
+julia> maximum(skipmissing(B), dims=2)
+2×1 Array{Int64,2}:
+ 1
+ 4
 ```
 """
 maximum(A::AbstractArray; dims)
@@ -490,6 +568,12 @@ Compute the minimum value of an array over the given dimensions. See also the
 [`min(a,b)`](@ref) function to take the minimum of two or more arguments,
 which can be applied elementwise to arrays via `min.(a,b)`.
 
+!!! note
+    If `A` contains `NaN` or [`missing`](@ref) values, they are propagated to the
+    corresponding result (`missing` takes precedence if a slice contains both).
+    Use [`skipmissing(A)`](@ref) to omit `missing` entries and compute the
+    minimum of non-missing values.
+
 # Examples
 ```jldoctest
 julia> A = [1 2; 3 4]
@@ -502,6 +586,20 @@ julia> minimum(A, dims=1)
  1  2
 
 julia> minimum(A, dims=2)
+2×1 Array{Int64,2}:
+ 1
+ 3
+
+julia> B = [1 missing; 3 4]
+2×2 Array{Union{Missing, Int64},2}:
+ 1   missing
+ 3  4
+
+julia> minimum(skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 1  4
+
+julia> minimum(skipmissing(B), dims=2)
 2×1 Array{Int64,2}:
  1
  3
@@ -635,6 +733,7 @@ for (fname, _fname, op) in [(:sum,     :_sum,     :add_sum), (:prod,    :_prod,
     @eval begin
         # User-facing methods with keyword arguments
         @inline ($fname)(a::AbstractArray; dims=:) = ($_fname)(a, dims)
+        @inline ($fname)(a::SkipMissing{<:AbstractArray}; dims=:) = ($_fname)(a, dims)
         @inline ($fname)(f::Callable, a::AbstractArray; dims=:) = ($_fname)(f, a, dims)
 
         # Underlying implementations using dispatch
diff --git a/doc/src/manual/missing.md b/doc/src/manual/missing.md
index 67b349f57a157..3b5bfa7420730 100644
--- a/doc/src/manual/missing.md
+++ b/doc/src/manual/missing.md
@@ -305,7 +305,36 @@ julia> mapreduce(sqrt, +, skipmissing([3, missing, 2, 1]))
 4.146264369941973
 ```
 
-Use [`collect`](@ref) to extract non-`missing` values and store them in an array
+Reduction over dimensions is also supported
+```jldoctest
+julia> B = [1 missing; 3 4]
+2×2 Array{Union{Missing, Int64},2}:
+ 1   missing
+ 3  4
+
+julia> sum(skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 4  4
+
+julia> sum(skipmissing(B), dims=2)
+2×1 Array{Int64,2}:
+ 1
+ 7
+
+julia> reduce(*, skipmissing(B), dims=1)
+1×2 Array{Int64,2}:
+ 3  4
+
+julia> mapreduce(cos, +, skipmissing(B), dims=1)
+1×2 Array{Float64,2}:
+ -0.44969  -0.653644
+```
+
+However, note that the special iterator object returned by `skipmissing` is not an
+`AbstractArray`: since `missing` entries of the original array are skipped,
+it does not have a regular shape and cannot be indexed.
+Use [`collect`](@ref) to extract non-`missing` values and store them in a vector,
+losing the shape of the original array
 ```jldoctest
 julia> collect(skipmissing([3, missing, 2, 1]))
 3-element Array{Int64,1}:
diff --git a/test/missing.jl b/test/missing.jl
index d25751322cb2e..0bae44ac7b890 100644
--- a/test/missing.jl
+++ b/test/missing.jl
@@ -412,6 +412,76 @@ end
             @test_throws ArgumentError mapreduce(x -> x/2, +, itr)
         end
     end
+
+    @testset "mapreduce over dims" begin
+        nm(x) = (@test !(eltype(x) >: Missing); x)
+        # Vary size to test splitting blocks with several configurations of missing values
+        for T in (Int, Float64),
+            A in (rand(T, 10), rand(T, 100, 1000), rand(T, 10000, 10)),
+            i in (1, 2, 1:2),
+            f in (identity, abs, abs2, cos),
+            (op, redf, init) in ((+, sum, x->oftype(f(one(eltype(x))), zero(eltype(x)))),
+                                  (*, prod, x->oftype(f(one(eltype(x))), one(eltype(x)))),
+                                  (max, maximum, x->f(first(skipmissing(x)))),
+                                  (min, minimum, x->f(first(skipmissing(x)))))
+            if T <: Integer
+                @test redf(A, dims=i) == nm(redf(skipmissing(A), dims=i)) ==
+                    nm(reduce(op, skipmissing(A), dims=i)) ==
+                    nm(mapreduce(identity, op, skipmissing(A), dims=i))
+            else
+                @test redf(A, dims=i) ≈ nm(redf(skipmissing(A), dims=i)) ==
+                    nm(reduce(op, skipmissing(A), dims=i)) ==
+                    nm(mapreduce(identity, op, skipmissing(A), dims=i))
+            end
+            @test mapreduce(f, op, A, dims=i) ≈
+                nm(mapreduce(f, op, skipmissing(A), dims=i))
+
+            maximum(i) > ndims(A) && (i = 1) # for mapslices
+            B = Array{Union{T,Missing}}(A)
+            replace!(x -> rand(Bool) ? x : missing, B)
+            # mapreduce fails for min and max if there are empty slices
+            if !(op in (min, max)) || !any(iszero, sum(!ismissing, B, dims=i))
+                if T === Int
+                    @test mapslices(x -> redf(skipmissing(x)), B, dims=i) ==
+                        nm(redf(skipmissing(B), dims=i))
+                else
+                    @test isapprox(mapslices(x -> redf(skipmissing(x)), B, dims=i),
+                        nm(redf(skipmissing(B), dims=i)), rtol=sqrt(eps()), atol=1e-16)
+                end
+                @test nm(redf(skipmissing(B), dims=i)) ==
+                    nm(reduce(op, skipmissing(B), dims=i)) ==
+                    nm(mapreduce(identity, op, skipmissing(B), dims=i))
+                @test isapprox(mapslices(x -> mapreduce(f, op, skipmissing(x), init=init(x)), B, dims=i),
+                               nm(mapreduce(f, op, skipmissing(B), dims=i)),
+                               rtol=sqrt(eps()), atol=1e-16)
+            elseif op in (min, max) && !(f in (abs, abs2))
+                @test_throws ArgumentError mapslices(x -> redf(skipmissing(x)), B, dims=i)
+                @test_throws ArgumentError redf(skipmissing(B), dims=i)
+                @test_throws ArgumentError reduce(op, skipmissing(B), dims=i)
+                @test_throws ArgumentError mapreduce(identity, op, skipmissing(B), dims=i)
+                @test_throws ArgumentError mapreduce(f, op, skipmissing(B), dims=i)
+            end
+
+            # Test block full of missing values
+            B[1:length(B)÷2] .= missing
+            if !(op in (min, max))
+                if T <: Integer
+                    @test mapslices(x -> redf(skipmissing(x)), B, dims=i) ==
+                        nm(redf(skipmissing(B), dims=i))
+                else
+                    @test isapprox(mapslices(x -> redf(skipmissing(x)), B, dims=i),
+                                   nm(redf(skipmissing(B), dims=i)),
+                                   atol=1e-16)
+                end
+                @test nm(redf(skipmissing(B), dims=i)) ==
+                    nm(reduce(op, skipmissing(B), dims=i)) ==
+                    nm(mapreduce(identity, op, skipmissing(B), dims=i))
+                @test isapprox(mapslices(x -> mapreduce(f, op, skipmissing(x), init=init(x)), B, dims=i),
+                               nm(mapreduce(f, op, skipmissing(B), dims=i)),
+                               rtol=sqrt(eps()), atol=1e-16)
+            end
+        end
+    end
 end
 
 @testset "coalesce" begin