diff --git a/base/missing.jl b/base/missing.jl
index 8166ade8d2401..8804b1b1ffc0f 100644
--- a/base/missing.jl
+++ b/base/missing.jl
@@ -23,12 +23,18 @@ nonmissingtype(::Type{Missing}) = Union{}
 nonmissingtype(::Type{T}) where {T} = T
 nonmissingtype(::Type{Any}) = Any
 
-promote_rule(::Type{Missing}, ::Type{T}) where {T} = Union{T, Missing}
-promote_rule(::Type{Union{S,Missing}}, ::Type{T}) where {T,S} = Union{promote_type(T, S), Missing}
-promote_rule(::Type{Any}, ::Type{T}) where {T} = Any
-promote_rule(::Type{Any}, ::Type{Missing}) = Any
-promote_rule(::Type{Missing}, ::Type{Any}) = Any
-promote_rule(::Type{Missing}, ::Type{Missing}) = Missing
+for U in (:Nothing, :Missing)
+    @eval begin
+        promote_rule(::Type{$U}, ::Type{T}) where {T} = Union{T, $U}
+        promote_rule(::Type{Union{S,$U}}, ::Type{T}) where {T,S} = Union{promote_type(T, S), $U}
+        promote_rule(::Type{Any}, ::Type{$U}) = Any
+        promote_rule(::Type{$U}, ::Type{Any}) = Any
+        promote_rule(::Type{$U}, ::Type{$U}) = U
+    end
+end
+promote_rule(::Type{Union{Nothing, Missing}}, ::Type{Any}) = Any
+promote_rule(::Type{Union{Nothing, Missing}}, ::Type{T}) where {T} =
+    Union{Nothing, Missing, T}
 
 convert(::Type{Union{T, Missing}}, x) where {T} = convert(T, x)
 # To fix ambiguities
diff --git a/base/namedtuple.jl b/base/namedtuple.jl
index 6606456a43462..353a8d4623325 100644
--- a/base/namedtuple.jl
+++ b/base/namedtuple.jl
@@ -55,6 +55,12 @@ indexed_next(t::NamedTuple, i::Int, state) = (getfield(t, i), i+1)
 isempty(::NamedTuple{()}) = true
 isempty(::NamedTuple) = false
 
+promote_rule(::Type{NamedTuple{n, S}}, ::Type{NamedTuple{n, T}}) where {n, S, T} =
+    NamedTuple{n, promote_type(S, T)}
+
+promote_join(::Type{NamedTuple{n, S}}, ::Type{NamedTuple{n, T}}) where {n, S, T} =
+    NamedTuple{n, promote_join(S, T)}
+
 convert(::Type{NamedTuple{names,T}}, nt::NamedTuple{names,T}) where {names,T} = nt
 convert(::Type{NamedTuple{names}}, nt::NamedTuple{names}) where {names} = nt
 
diff --git a/base/promotion.jl b/base/promotion.jl
index ba5ee0fd74e4e..9f59ce38a2adf 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -5,30 +5,35 @@
 """
     typejoin(T, S)
 
-Return the closest common ancestor of `T` and `S`, i.e. a type which
-contains both of them.
+
+Return the closest common ancestor of `T` and `S`, i.e. the narrowest type from which
+they both inherit.
 """
 typejoin() = (@_pure_meta; Bottom)
 typejoin(@nospecialize(t)) = (@_pure_meta; t)
 typejoin(@nospecialize(t), ts...) = (@_pure_meta; typejoin(t, typejoin(ts...)))
-function typejoin(@nospecialize(a), @nospecialize(b))
+typejoin(@nospecialize(a), @nospecialize(b)) = join_types(a, b, typejoin)
+
+function join_types(@nospecialize(a), @nospecialize(b), f::Function)
     @_pure_meta
     if a <: b
         return b
     elseif b <: a
         return a
     elseif isa(a,UnionAll)
-        return UnionAll(a.var, typejoin(a.body, b))
+        return UnionAll(a.var, join_types(a.body, b, f))
     elseif isa(b,UnionAll)
-        return UnionAll(b.var, typejoin(a, b.body))
+        return UnionAll(b.var, join_types(a, b.body, f))
     elseif isa(a,TypeVar)
-        return typejoin(a.ub, b)
+        return f(a.ub, b)
     elseif isa(b,TypeVar)
-        return typejoin(a, b.ub)
+        return f(a, b.ub)
     elseif isa(a,Union)
-        return typejoin(typejoin(a.a,a.b), b)
+        a′ = f(a.a,a.b)
+        return a′ === a ? typejoin(a, b) : f(a′, b)
     elseif isa(b,Union)
-        return typejoin(a, typejoin(b.a,b.b))
+        b′ = f(b.a,b.b)
+        return b′ === b ? typejoin(a, b) : f(a, b′)
     elseif a <: Tuple
         if !(b <: Tuple)
             return Any
@@ -36,31 +41,31 @@ function typejoin(@nospecialize(a), @nospecialize(b))
         ap, bp = a.parameters, b.parameters
         lar = length(ap)::Int; lbr = length(bp)::Int
         if lar == 0
-            return Tuple{Vararg{tailjoin(bp,1)}}
+            return Tuple{Vararg{tailjoin(bp,1,f)}}
         end
         if lbr == 0
-            return Tuple{Vararg{tailjoin(ap,1)}}
+            return Tuple{Vararg{tailjoin(ap,1,f)}}
         end
         laf, afixed = full_va_len(ap)
         lbf, bfixed = full_va_len(bp)
         if laf < lbf
             if isvarargtype(ap[lar]) && !afixed
                 c = Vector{Any}(uninitialized, laf)
-                c[laf] = Vararg{typejoin(unwrapva(ap[lar]), tailjoin(bp,laf))}
+                c[laf] = Vararg{f(unwrapva(ap[lar]), tailjoin(bp,laf,f))}
                 n = laf-1
             else
                 c = Vector{Any}(uninitialized, laf+1)
-                c[laf+1] = Vararg{tailjoin(bp,laf+1)}
+                c[laf+1] = Vararg{tailjoin(bp,laf+1,f)}
                 n = laf
             end
         elseif lbf < laf
             if isvarargtype(bp[lbr]) && !bfixed
                 c = Vector{Any}(uninitialized, lbf)
-                c[lbf] = Vararg{typejoin(unwrapva(bp[lbr]), tailjoin(ap,lbf))}
+                c[lbf] = Vararg{f(unwrapva(bp[lbr]), tailjoin(ap,lbf,f))}
                 n = lbf-1
             else
                 c = Vector{Any}(uninitialized, lbf+1)
-                c[lbf+1] = Vararg{tailjoin(ap,lbf+1)}
+                c[lbf+1] = Vararg{tailjoin(ap,lbf+1,f)}
                 n = lbf
             end
         else
@@ -69,7 +74,7 @@ function typejoin(@nospecialize(a), @nospecialize(b))
         end
         for i = 1:n
             ai = ap[min(i,lar)]; bi = bp[min(i,lbr)]
-            ci = typejoin(unwrapva(ai),unwrapva(bi))
+            ci = f(unwrapva(ai),unwrapva(bi))
             c[i] = i == length(c) && (isvarargtype(ai) || isvarargtype(bi)) ? Vararg{ci} : ci
         end
         return Tuple{c...}
@@ -110,10 +115,10 @@ Compute a type that contains both `T` and `S`, which could be
 either a parent of both types, or a `Union` if appropriate.
 Falls back to [`typejoin`](@ref).
 """
-promote_join(@nospecialize(a), @nospecialize(b)) = typejoin(a, b)
+promote_join(@nospecialize(a), @nospecialize(b)) = join_types(a, b, promote_join)
 promote_join(::Type{Nothing}, ::Type{T}) where {T} =
     isconcrete(T) ? Union{T, Nothing} : Any
-promote_join(::Type{T}, ::Type{Void}) where {T} =
+promote_join(::Type{T}, ::Type{Nothing}) where {T} =
     isconcrete(T) ? Union{T, Nothing} : Any
 promote_join(::Type{Missing}, ::Type{T}) where {T} =
     isconcrete(T) ? Union{T, Missing} : Any
@@ -138,14 +143,14 @@ function full_va_len(p)
     return length(p)::Int, true
 end
 
-# reduce typejoin over A[i:end]
-function tailjoin(A, i)
+# reduce join_types over A[i:end]
+function tailjoin(A, i, f::Function)
     if i > length(A)
         return unwrapva(A[end])
     end
     t = Bottom
     for j = i:length(A)
-        t = typejoin(t, unwrapva(A[j]))
+        t = f(t, unwrapva(A[j]))
     end
     return t
 end
@@ -215,6 +220,10 @@ it for new types as appropriate.
 function promote_rule end
 
 promote_rule(::Type{<:Any}, ::Type{<:Any}) = Bottom
+# To fix ambiguities
+promote_rule(::Type{Any}, ::Type{<:Any}) = Any
+promote_rule(::Type{<:Any}, ::Type{Any}) = Any
+promote_rule(::Type{Any}, ::Type{Any}) = Any
 
 promote_result(::Type{<:Any},::Type{<:Any},::Type{T},::Type{S}) where {T,S} = (@_inline_meta; promote_type(T,S))
 # If no promote_rule is defined, both directions give Bottom. In that
diff --git a/base/set.jl b/base/set.jl
index 28f288f1aef35..f748a4e97f364 100644
--- a/base/set.jl
+++ b/base/set.jl
@@ -142,6 +142,7 @@ function union!(s::Set{T}, itr) where T
     s
 end
 
+
 """
     intersect(s, itrs...)
     ∩(s, itrs...)
diff --git a/base/tuple.jl b/base/tuple.jl
index 22e4bd249eb26..2833a18b802a2 100644
--- a/base/tuple.jl
+++ b/base/tuple.jl
@@ -87,6 +87,11 @@ function _compute_eltype(t::Type{<:Tuple})
     return r
 end
 
+# promotion
+
+promote_rule(::Type{S}, ::Type{T}) where {S<:Tuple, T<:Tuple} =
+    join_types(S, T, promote_type)
+
 # version of tail that doesn't throw on empty tuples (used in array indexing)
 safe_tail(t::Tuple) = tail(t)
 safe_tail(t::Tuple{}) = ()
diff --git a/base/twiceprecision.jl b/base/twiceprecision.jl
index bc47ea3f2bb6d..305d3a8c507cd 100644
--- a/base/twiceprecision.jl
+++ b/base/twiceprecision.jl
@@ -237,7 +237,7 @@ eltype(::Type{TwicePrecision{T}}) where {T} = T
 
 promote_rule(::Type{TwicePrecision{R}}, ::Type{TwicePrecision{S}}) where {R,S} =
     TwicePrecision{promote_type(R,S)}
-promote_rule(::Type{TwicePrecision{R}}, ::Type{S}) where {R,S} =
+promote_rule(::Type{TwicePrecision{R}}, ::Type{S}) where {R,S<:Number} =
     TwicePrecision{promote_type(R,S)}
 
 (::Type{T})(x::TwicePrecision) where {T<:Number} = T(x.hi + x.lo)::T
diff --git a/stdlib/Test/test/runtests.jl b/stdlib/Test/test/runtests.jl
index 12eb63e0386c3..4231f410c3650 100644
--- a/stdlib/Test/test/runtests.jl
+++ b/stdlib/Test/test/runtests.jl
@@ -107,7 +107,7 @@ let fails = @testset NoThrowTestSet begin
         @test isapprox(1 / 2, 2 / 1, atol=1 / 1)
         @test isapprox(1 - 2, 2 - 1; atol=1 - 1)
         # Fail - function keyword splatting
-        k = [(:atol, 0), (:nans, true)]
+        k = Any[(:atol, 0), (:nans, true)]
         @test isapprox(1, 2; k...)
         # Error - unexpected pass
         @test_broken true
diff --git a/test/abstractarray.jl b/test/abstractarray.jl
index ccbbfd3f67b79..ac4a2afac5eeb 100644
--- a/test/abstractarray.jl
+++ b/test/abstractarray.jl
@@ -625,7 +625,7 @@ function test_cat(::Type{TestAbstractArray})
     @test @inferred(vcat([1.0, 2.0], 3))::Array{Float64,1} == [1.0, 2.0, 3.0]
 
     @test @inferred(vcat(["a"], "b"))::Vector{String} == ["a", "b"]
-    @test @inferred(vcat((1,), (2.0,)))::Vector{Tuple{Real}} == [(1,), (2.0,)]
+    @test @inferred(vcat((1,), (2.0,)))::Vector{Tuple{Float64}} == [(1,), (2.0,)]
 end
 
 function test_ind2sub(::Type{TestAbstractArray})
diff --git a/test/ambiguous.jl b/test/ambiguous.jl
index 1654f88360215..77c64bacfa86c 100644
--- a/test/ambiguous.jl
+++ b/test/ambiguous.jl
@@ -289,6 +289,7 @@ end
         pop!(need_to_handle_undef_sparam, which(Base.cat, (Any, SparseArrays._TypedDenseConcatGroup{T} where T)))
         pop!(need_to_handle_undef_sparam, which(Base.float, Tuple{AbstractArray{Union{Missing, T},N} where {T, N}}))
         pop!(need_to_handle_undef_sparam, which(Base.convert, Tuple{Type{Union{Missing, T}} where T, Any}))
+        pop!(need_to_handle_undef_sparam, which(Base.promote_rule, Tuple{Type{Union{Nothing, S}} where S, Type{T} where T}))
         pop!(need_to_handle_undef_sparam, which(Base.promote_rule, Tuple{Type{Union{Missing, S}} where S, Type{T} where T}))
         pop!(need_to_handle_undef_sparam, which(Base.zero, Tuple{Type{Union{Missing, T}} where T}))
         pop!(need_to_handle_undef_sparam, which(Base.one, Tuple{Type{Union{Missing, T}} where T}))
diff --git a/test/arrayops.jl b/test/arrayops.jl
index 9082863fbaa10..b681c3d7ebfbc 100644
--- a/test/arrayops.jl
+++ b/test/arrayops.jl
@@ -1206,7 +1206,7 @@ end
     @test isequal([1,2,3], [a for (a,b) in enumerate(2:4)])
     @test isequal([2,3,4], [b for (a,b) in enumerate(2:4)])
 
-    @test [s for s in Union{String, Void}["a", nothing]] isa Vector{Union{String, Void}}
+    @test [s for s in Union{String, Nothing}["a", nothing]] isa Vector{Union{String, Nothing}}
     @test [s for s in Union{String, Missing}["a", missing]] isa Vector{Union{String, Missing}}
 
     @testset "comprehension in let-bound function" begin
diff --git a/test/bitarray.jl b/test/bitarray.jl
index 214484dcebc7f..cbfc41994913e 100644
--- a/test/bitarray.jl
+++ b/test/bitarray.jl
@@ -2,7 +2,7 @@
 
 using Base: findprevnot, findnextnot
 
-tc(r1::NTuple{N,Any}, r2::NTuple{N,Any}) where {N} = all(x->tc(x...), [zip(r1,r2)...])
+tc(r1::NTuple{N,Any}, r2::NTuple{N,Any}) where {N} = all(x->tc(x...), Any[zip(r1,r2)...])
 tc(r1::BitArray{N}, r2::Union{BitArray{N},Array{Bool,N}}) where {N} = true
 tc(r1::Transpose{Bool,BitVector}, r2::Union{Transpose{Bool,BitVector},Transpose{Bool,Vector{Bool}}}) = true
 tc(r1::T, r2::T) where {T} = true
@@ -854,10 +854,10 @@ timesofar("unary arithmetic")
         @check_bit_operation broadcast(-, u1, b2)  Matrix{UInt8}
         @check_bit_operation broadcast(*, u1, b2) Matrix{UInt8}
 
-        for (x1,t1) = [(f1, Float64),
-                       (ci1, Complex{Int}),
-                       (cu1, Complex{UInt8}),
-                       (cf1, ComplexF64)]
+        for (x1,t1) = Any[(f1, Float64),
+                          (ci1, Complex{Int}),
+                          (cu1, Complex{UInt8}),
+                          (cf1, ComplexF64)]
             @check_bit_operation broadcast(+, x1, b2)  Matrix{t1}
             @check_bit_operation broadcast(-, x1, b2)  Matrix{t1}
             @check_bit_operation broadcast(*, x1, b2) Matrix{t1}
diff --git a/test/core.jl b/test/core.jl
index 7001daa5f4bb4..f478c10982c81 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -125,8 +125,8 @@ end
 @test typejoin(Tuple{Vararg{Int,2}}, Tuple{Int,Int,Int}) === Tuple{Int,Int,Vararg{Int}}
 @test typejoin(Tuple{Vararg{Int,2}}, Tuple{Vararg{Int}}) === Tuple{Vararg{Int}}
 
-# promote_join returns a Union only with Void/Missing combined with concrete types
-for T in (Void, Missing)
+# promote_join returns a Union only with Nothing/Missing combined with concrete types
+for T in (Nothing, Missing)
     @test Base.promote_join(Int, Float64) === Real
     @test Base.promote_join(Int, T) === Union{Int, T}
     @test Base.promote_join(T, String) === Union{T, String}
diff --git a/test/functional.jl b/test/functional.jl
index 2410094633c55..a42d001f72e6f 100644
--- a/test/functional.jl
+++ b/test/functional.jl
@@ -151,27 +151,26 @@ end
                  for p = 100-q-d-n
                  if p < n < d < q] == [(50,30,15,5), (50,30,20,0), (50,40,10,0), (75,20,5,0)]
 
-@testset "map/collect return type on generators with $T" for (T, v) in ((Void, nothing),
-                                                                        (Missing, missing))
+@testset "map/collect return type on generators with $T" for T in (Nothing, Missing)
     x = ["a", "b"]
     res = @inferred collect(s for s in x)
     @test res isa Vector{String}
     res = @inferred map(identity, x)
     @test res isa Vector{String}
-    res = @inferred collect(s === v for s in x)
+    res = @inferred collect(s isa T for s in x)
     @test res isa Vector{Bool}
-    res = @inferred map(s -> s === v, x)
+    res = @inferred map(s -> s isa T, x)
     @test res isa Vector{Bool}
-    y = Union{String, T}["a", v]
-    f(s::Union{Void, Missing}) = s
+    y = Union{String, T}["a", T()]
+    f(s::Union{Nothing, Missing}) = s
     f(s::String) = s == "a"
     res = collect(s for s in y)
     @test res isa Vector{Union{String, T}}
     res = map(identity, y)
     @test res isa Vector{Union{String, T}}
-    res = @inferred collect(s === v for s in y)
+    res = @inferred collect(s isa T for s in y)
     @test res isa Vector{Bool}
-    res = @inferred map(s -> s === v, y)
+    res = @inferred map(s -> s isa T, y)
     @test res isa Vector{Bool}
     res = collect(f(s) for s in y)
     @test res isa Vector{Union{Bool, T}}
diff --git a/test/missing.jl b/test/missing.jl
index 960edeaaf74ff..69d1f88bbb678 100644
--- a/test/missing.jl
+++ b/test/missing.jl
@@ -40,6 +40,16 @@ end
     @test_broken promote_type(Union{Nothing, Missing, Int}, Float64) == Any
 end
 
+@testset "promotion in various contexts" for T in (Nothing, Missing)
+    @test collect(v for v in (1, T())) isa Vector{Union{Int,T}}
+    @test map(identity, Any[1, T()]) isa Vector{Union{Int,T}}
+    @test broadcast(identity, Any[1, T()]) isa Vector{Union{Int,T}}
+    @test unique((1, T())) isa Vector{Union{Int,T}}
+
+    @test map(ismissing, Any[1, missing]) isa Vector{Bool}
+    @test broadcast(ismissing, Any[1, missing]) isa BitVector
+end
+
 @testset "comparison operators" begin
     @test (missing == missing) === missing
     @test (1 == missing) === missing
diff --git a/test/namedtuple.jl b/test/namedtuple.jl
index df5e5d274e3f3..8d910136be8cf 100644
--- a/test/namedtuple.jl
+++ b/test/namedtuple.jl
@@ -212,4 +212,32 @@ abstr_nt_22194_3()
 @test @inferred find(equalto(1), (a=1, b=2)) == [:a]
 @test @inferred find(equalto(1), (a=1, b=1)) == [:a, :b]
 @test @inferred isempty(find(equalto(1), NamedTuple()))
-@test @inferred isempty(find(equalto(1), (a=2, b=3)))
\ No newline at end of file
+@test @inferred isempty(find(equalto(1), (a=2, b=3)))
+
+# Test promotion
+
+@test promote_type(NamedTuple{(:a,),Tuple{Int}},
+                   NamedTuple{(:a,),Tuple{Float64}}) ===
+    NamedTuple{(:a,),Tuple{Float64}}
+@test promote_type(NamedTuple{(:a,:b),Tuple{Int,Float64}},
+                   NamedTuple{(:a,:b),Tuple{Float64,Int}}) ===
+    NamedTuple{(:a, :b),Tuple{Float64, Float64}}
+@test promote_type(NamedTuple{(:a,:b),Tuple{Int,String}},
+                   NamedTuple{(:a,:b),Tuple{Float64,Int}}) ===
+    NamedTuple{(:a,:b),Tuple{Float64,Any}}
+
+for T in (Nothing, Missing)
+    @test promote_type(NamedTuple{(:a,:b),Tuple{Int,Int}},
+                       NamedTuple{(:a,:b),Tuple{T,Union{Float64,T}}}) ===
+        NamedTuple{(:a,:b),Tuple{Union{Int, T},Union{Float64,T}}}
+
+    x = [(a=1, b=T()), (a=1, b=2)]
+    @test x isa Vector{NamedTuple{(:a,:b),Tuple{Int,Union{T,Int}}}}
+
+    y = map(v -> (a=v.a, b=v.b), [(a=1, b=T()), (a=1, b=2)])
+    @test y isa Vector{NamedTuple{(:a,:b),Tuple{Int,Union{T,Int}}}}
+    @test isequal(x, y)
+end
+y = map(v -> (a=v.a, b=v.a + v.b), [(a=1, b=missing), (a=1, b=2)])
+@test y isa Vector{NamedTuple{(:a,:b),Tuple{Int,Union{Missing,Int}}}}
+@test isequal(y, [(a=1, b=missing), (a=1, b=3)])
\ No newline at end of file
diff --git a/test/tuple.jl b/test/tuple.jl
index f7f5d0260da31..2eab4c0ddaa6a 100644
--- a/test/tuple.jl
+++ b/test/tuple.jl
@@ -181,6 +181,29 @@ end
         typejoin(Int, AbstractFloat, Bool)
     @test eltype(Union{Tuple{Int, Float64}, Tuple{Vararg{Bool}}}) ===
         typejoin(Int, Float64, Bool)
+    @test eltype(Tuple{Int, Missing}) === Union{Missing, Int}
+    @test eltype(Tuple{Int, Nothing}) === Union{Nothing, Int}
+end
+
+@testset "promotion" begin
+    @test promote_type(Tuple{Int}, Tuple{Float64}) === Tuple{Float64}
+    @test promote_type(Tuple{Int,Float64}, Tuple{Float64,Int}) === Tuple{Float64,Float64}
+    @test promote_type(Tuple{Int,String}, Tuple{Float64,Int}) === Tuple{Float64,Any}
+
+    for T in (Nothing, Missing)
+        @test promote_type(Tuple{Int,Int}, Tuple{T,Union{T,Float64}}) ===
+            Tuple{Union{Int,T},Union{Float64,T}}
+
+        x = [(1, T()), (1, 2)]
+        @test x isa Vector{Tuple{Int,Union{Int,T}}}
+
+        y = map(v -> (v[1], v[2]), [(1, T()), (1, 2)])
+        @test y isa Vector{Tuple{Int,Union{T,Int}}}
+        @test isequal(x, y)
+    end
+    y = map(v -> (v[1], v[1] + v[2]), [(1, missing), (1, 2)])
+    @test y isa Vector{Tuple{Int,Union{Missing,Int}}}
+    @test isequal(y, [(1, missing), (1, 3)])
 end
 
 @testset "mapping" begin