diff --git a/src/AxisArrays.jl b/src/AxisArrays.jl
index 72fe295..8676055 100644
--- a/src/AxisArrays.jl
+++ b/src/AxisArrays.jl
@@ -22,5 +22,8 @@ include("indexing.jl")
 include("sortedvector.jl")
 include("categoricalvector.jl")
 include("combine.jl")
+@static if VERSION >= v"0.7.0-DEV.2638"
+    include("broadcast.jl")
+end
 
 end
diff --git a/src/broadcast.jl b/src/broadcast.jl
new file mode 100644
index 0000000..279a5c9
--- /dev/null
+++ b/src/broadcast.jl
@@ -0,0 +1,61 @@
+Base.BroadcastStyle(::Type{<:AxisArray}) = Broadcast.ArrayStyle{AxisArray}()
+Base.BroadcastStyle(::Type{<:Adjoint{T, <:AxisArray{T}}}) where T =
+    Broadcast.ArrayStyle{AxisArray}()
+
+# Hijack broadcasting after determining style
+function Base.broadcast(f, ::Broadcast.ArrayStyle{AxisArray}, ::Nothing, ::Nothing, As...)
+    # We need to make sure we can combine indices of only the AxisArrays before attempting
+    # broadcasting. The total broadcasting operation may include other AbstractArrays.
+    # We demand that for a given dimension, the axes values and names must match
+    # as implemented, this demands exact matching of axes (even floating point nums).
+    axesAs = Broadcast.combine_indices(axarrs(As)...)
+
+    # Obtain the underlying data and find the result indices if we were to
+    # broadcast all arrays without axis info.
+    Bs = data(As)
+
+    # Broadcast using the underlying data
+    broadcasted = broadcast(f, Bs...)
+
+    defaxesBs = default_axes(broadcasted)
+    axesBs = broadcax(axesAs, defaxesBs)
+    return AxisArray(broadcasted, axesBs)
+end
+
+broadcax(axes::Tuple, defaxes::Tuple) =
+    (broadcax1(axes[1], defaxes[1]), broadcax(tail(axes), tail(defaxes))...)
+broadcax(axes::Tuple{}, defaxes::Tuple) = ()
+broadcax1(::Tuple{}, x) = ()
+function broadcax1(axA::Axis, axB::Axis)
+    axAname, axAvalues = axisname(axA), axisvalues(axA)[1]
+    axAname != axisname(axB) && return axA
+    if typeof(axAvalues) <: Base.OneTo
+        # We believe this was a default axis, not just an axis that happened to
+        # have the default name
+        return typeof(axA)(Base.OneTo(length(axB)))
+    else
+        error("axis values did not match.")
+    end
+end
+
+# Compares the value indices and axis names (note: AxisArrays.axes, not Base.axes)
+Broadcast.broadcast_indices(::Broadcast.ArrayStyle{AxisArray}, A) = axes(A)
+Broadcast.broadcast_indices(::Broadcast.ArrayStyle{AxisArray}, A::Adjoint{T,S}) where
+    {T, S<:AxisArray{T,1}} = (Axis{:row}(Base.OneTo(1)), axes(A.parent)[1])
+Broadcast.broadcast_indices(::Broadcast.ArrayStyle{AxisArray}, A::Adjoint{T,S}) where
+    {T, S<:AxisArray{T,2}} = tupswap(axes(A.parent))
+
+# Helper functions
+# Given a tuple `A`, return a tuple containing only the AxisArrays (or their adjoints) in `A`
+axarrs(A::Tuple{AxisArray, Vararg}) = (A[1], axarrs(Base.tail(A))...)
+axarrs(A::Tuple{Adjoint{T, <:AxisArray} where T, Vararg}) = (A[1], axarrs(Base.tail(A))...)
+axarrs(A::Tuple{Any, Vararg}) = axarrs(Base.tail(A))
+axarrs(A::Tuple{}) = ()
+
+data(A::Tuple{AxisArray,Vararg}) = (A[1].data, data(Base.tail(A))...)
+data(A::Tuple{Adjoint{T, <:AxisArray} where T, Vararg}) =
+    (adjoint(A[1].parent.data), data(Base.tail(A))...)
+data(A::Tuple{Any,Vararg}) = (A[1], data(Base.tail(A))...)
+data(A::Tuple{}) = ()
+
+tupswap(A::Tuple{Any,Any}) = (A[2],A[1])
diff --git a/test/broadcast.jl b/test/broadcast.jl
new file mode 100644
index 0000000..26385b7
--- /dev/null
+++ b/test/broadcast.jl
@@ -0,0 +1,144 @@
+A0 = [1,2,3]
+A  = AxisArray(A0, Axis{:abc}([1.0, 2.0, 3.0]))
+A1 = AxisArray(A0, Axis{:def}([1.0, 2.0, 3.0]))
+A2 = AxisArray(A0, Axis{:abc}([1.0, 2.0, 3.0+eps(3.0)]))
+
+B0 = [1 2 3]
+B  = AxisArray(B0, Axis{:row}(Base.OneTo(1)), Axis{:def}([1.3, 2.4, 36]))
+B1 = AxisArray(B0, Axis{:row}(Base.OneTo(1)),  Axis{:abc}([1.0, 2.0, 3.0]))
+B2 = AxisArray(B0, Axis{:abc}(Base.OneTo(1)), Axis{:def}([1.3, 2.4, 36]))
+
+C0 = reshape([10])
+C  = AxisArray(C0)
+
+D0 = ones(Complex, 3, 3)
+D  = AxisArray(D0, Axis{:abc}([1.0, 2.0, 3.0]), Axis{:def}([1.3, 2.4, 36]))
+D1 = AxisArray(D0, Axis{:abc}([1.0, 2.0, 3.0+eps(3.0)]), Axis{:def}([1.3, 2.4, 36]))
+D2 = AxisArray(D0, Axis{:row}(Base.OneTo(3)), Axis{:def}([1.3, 2.4, 36]))
+D3 = AxisArray(D0, Axis{:abc}([1.0, 2.0, 3.1]), Axis{:def}([1.3, 2.4, 36]))
+
+# AxisArray 0-d + number
+@test (C .+ 1) isa AxisArray
+@test @inferred(C .+ 1).data == reshape([11])
+@test AxisArrays.axes(C .+ 1) == ()
+@test (1 .+ C) isa AxisArray
+@test @inferred(1 .+ C).data == reshape([11])
+@test AxisArrays.axes(1 .+ C) == ()
+
+# AxisArray vector + number
+@test (A .+ 1) isa AxisArray
+@test @inferred(A .+ 1).data == [2,3,4]
+@test AxisArrays.axes(A .+ 1)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test (1 .+ A) isa AxisArray
+@test @inferred(1 .+ A).data == [2,3,4]
+@test AxisArrays.axes(1 .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+
+# AxisArray row-vector + number...
+# AxisArray matrix + number...
+# AxisArray higher-d + number...
+
+# AxisArray 0-d + AxisArray 0-d
+@test (C .+ C) isa AxisArray
+@test @inferred(C .+ C).data == reshape([20])
+@test AxisArrays.axes(C .+ C) == ()
+
+# AxisArray 0-d + non-AxisArray 0-d
+@test (C0 .+ C) isa AxisArray
+@test @inferred(C0 .+ C).data == reshape([20])
+@test AxisArrays.axes(C0 .+ C) == ()
+@test (C .+ C0) isa AxisArray
+@test @inferred(C .+ C0).data == reshape([20])
+@test AxisArrays.axes(C .+ C0) == ()
+
+# AxisArray vector + AxisArray 0-d
+@test @inferred(A .+ C).data == [11,12,13]
+@test AxisArrays.axes(A .+ C)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test length(AxisArrays.axes(A .+ C)) == 1
+@test @inferred(C .+ A).data == [11,12,13]
+@test AxisArrays.axes(C .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test length(AxisArrays.axes(C .+ A)) == 1
+
+# AxisArray vector + non-AxisArray 0-d
+@test @inferred(A .+ C0).data == [11,12,13]
+@test AxisArrays.axes(A .+ C0)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test length(AxisArrays.axes(A .+ C0)) == 1
+@test @inferred(C0 .+ A).data == [11,12,13]
+@test AxisArrays.axes(C0 .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test length(AxisArrays.axes(C0 .+ A)) == 1
+
+# AxisArray vector + AxisArray vector
+@test @inferred(A .+ A).data == [2,4,6]
+@test AxisArrays.axes(A .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test length(AxisArrays.axes(A .+ A)) == 1
+@test_throws DimensionMismatch (A.+A1)      # axis name mismatch
+@test_throws DimensionMismatch (A1.+A)
+@test_throws DimensionMismatch (A.+A2)      # axis value mismatch (floating-points count)
+@test_throws DimensionMismatch (A2.+A)
+
+# AxisArray vector + non-AxisArray vector
+@test @inferred(A .+ A0).data == [2,4,6]
+@test AxisArrays.axes(A .+ A0)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test length(AxisArrays.axes(A .+ A0)) == 1
+@test @inferred(A0 .+ A).data == [2,4,6]
+@test AxisArrays.axes(A0 .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test length(AxisArrays.axes(A0 .+ A)) == 1
+
+# AxisArray vector + 1xN AxisArray matrix
+@test_broken @inferred(A .+ B).data == [2 3 4; 3 4 5; 4 5 6]   # output good but axes aren't yet inferred...
+@test length(AxisArrays.axes(A .+ B)) == 2
+@test AxisArrays.axes(A .+ B)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test AxisArrays.axes(A .+ B)[2] == Axis{:def}([1.3, 2.4, 36])
+
+@test_broken @inferred(B .+ A).data == [2 3 4; 3 4 5; 4 5 6]   # output good but axes aren't yet inferred...
+@test length(AxisArrays.axes(B .+ A)) == 2
+@test AxisArrays.axes(B .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test AxisArrays.axes(B .+ A)[2] == Axis{:def}([1.3, 2.4, 36])
+
+@test_throws ArgumentError (A.+B1)  # axis names don't match
+@test_throws ArgumentError (B1.+A)
+@test_broken @test_throws DimensionMismatch (A.+B2)
+@test_broken @test_throws DimensionMismatch (B2.+A)
+
+# AxisArray vector + 1xN non-AxisArray matrix
+@test @inferred(A.+B0).data == [2 3 4; 3 4 5; 4 5 6]
+@test length(AxisArrays.axes(A .+ B0)) == 2
+@test AxisArrays.axes(A .+ B0)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test AxisArrays.axes(A .+ B0)[2] == Axis{:col}(Base.OneTo(3))
+
+# AxisArray vector + NxN AxisArray matrix
+@test_broken @inferred(A .+ D).data ==
+    [2+0im 2+0im 2+0im;
+     3+0im 3+0im 3+0im;
+     4+0im 4+0im 4+0im] # output good but inference dies
+@test length(AxisArrays.axes(A .+ D)) == 2
+@test AxisArrays.axes(A .+ D)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test AxisArrays.axes(A .+ D)[2] == Axis{:def}([1.3, 2.4, 36])
+@test_broken @inferred(D .+ A).data ==
+    [2+0im 2+0im 2+0im;
+     3+0im 3+0im 3+0im;
+     4+0im 4+0im 4+0im] # output good but inference dies
+@test length(AxisArrays.axes(D .+ A)) == 2
+@test AxisArrays.axes(D .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test AxisArrays.axes(D .+ A)[2] == Axis{:def}([1.3, 2.4, 36])
+@test_throws DimensionMismatch (A.+D1)
+@test_throws DimensionMismatch (D1.+A)
+@test_throws DimensionMismatch (A.+D2)
+@test_throws DimensionMismatch (D2.+A)
+@test_throws DimensionMismatch (A.+D3)
+@test_throws DimensionMismatch (D3.+A)
+
+# AxisArray vector + NxN non-AxisArray matrix
+@test_broken @inferred(A .+ D0).data ==
+    [2+0im 2+0im 2+0im;
+     3+0im 3+0im 3+0im;
+     4+0im 4+0im 4+0im] # output good but inference dies
+@test length(AxisArrays.axes(A .+ D0)) == 2
+@test AxisArrays.axes(A .+ D0)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test AxisArrays.axes(A .+ D0)[2] == Axis{:col}(Base.OneTo(3))
+@test_broken @inferred(D0 .+ A).data ==
+    [2+0im 2+0im 2+0im;
+     3+0im 3+0im 3+0im;
+     4+0im 4+0im 4+0im] # output good but inference dies
+@test length(AxisArrays.axes(D0 .+ A)) == 2
+@test AxisArrays.axes(D0 .+ A)[1] == Axis{:abc}([1.0, 2.0, 3.0])
+@test AxisArrays.axes(D0 .+ A)[2] == Axis{:col}(Base.OneTo(3))
diff --git a/test/runtests.jl b/test/runtests.jl
index ddbe50b..99097a8 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -34,6 +34,12 @@ import IterTools
         include("combine.jl")
     end
 
+    @static if VERSION >= v"0.7.0-DEV.2638"
+        @testset "Broadcast" begin
+            include("broadcast.jl")
+        end
+    end
+
     @testset "README" begin
         include("readme.jl")
     end