diff --git a/docs/src/api.md b/docs/src/api.md
index 8be04bc66..80901efb6 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -113,6 +113,8 @@ data
 dimnum
 dims
 hasdim
+otherdims
+commondims
 label
 mode
 metadata
@@ -121,6 +123,7 @@ refdims
 shortname
 units
 val
+basetypeof
 ```
 
 And some utility methods for transforming DimensionalData objects:
@@ -128,11 +131,18 @@ And some utility methods for transforming DimensionalData objects:
 ```@docs
 rebuild
 modify
+dimwise
+dimwise!
 setdims
 swapdims
 reorderindex
 reorderarray
 reorderrelation
+reverseindex
+reversearray
+flipindex
+fliparray
+fliprelation
 ```
 
 ## Non-exported methods for developers
diff --git a/src/DimensionalData.jl b/src/DimensionalData.jl
index 7d970a085..6483e0c39 100644
--- a/src/DimensionalData.jl
+++ b/src/DimensionalData.jl
@@ -45,7 +45,8 @@ export AbstractDimArray, DimArray, AbstractDimensionalArray, DimensionalArray
 export data, dims, refdims, mode, metadata, name, shortname,
        val, label, units, order, bounds, locus, mode, <|
 
-export dimnum, hasdim, setdims, swapdims, rebuild, modify
+export dimnum, hasdim, otherdims, commondims, setdims, swapdims, rebuild, 
+       modify, dimwise, dimwise!
 
 export order, indexorder, arrayorder, 
        reverseindex, reversearray, reorderindex, 
diff --git a/src/dimension.jl b/src/dimension.jl
index b6f82777f..677bf8d94 100644
--- a/src/dimension.jl
+++ b/src/dimension.jl
@@ -171,6 +171,7 @@ Base.size(dim::Dimension) = size(val(dim))
 Base.size(dim::Dimension{<:Val}) = (length(unwrap(val(dim))),)
 Base.axes(dim::Dimension) = axes(val(dim))
 Base.axes(dim::Dimension{<:Val}) = (Base.OneTo(length(dim)),)
+Base.axes(dim::Dimension, i) = axes(val(dim), i)
 Base.eachindex(dim::Dimension) = eachindex(val(dim))
 Base.length(dim::Dimension{<:Union{AbstractArray,Number}}) = length(val(dim))
 Base.length(dim::Dimension{<:Val}) = length(unwrap(val(dim)))
diff --git a/src/primitives.jl b/src/primitives.jl
index 72b1a1890..903ddbf23 100644
--- a/src/primitives.jl
+++ b/src/primitives.jl
@@ -20,7 +20,7 @@ const UnionAllTupleOrVector = Union{Vector{UnionAll},Tuple{UnionAll,Vararg}}
 @inline _sortdims(tosort::Tuple, order::Tuple, rejected) =
     # Match dims to the order, and also check if the mode has a
     # transformed dimension that matches
-    if _dimsmatch(tosort[1], order[1])
+    if dimsmatch(tosort[1], order[1])
         (tosort[1], _sortdims((rejected..., tail(tosort)...), tail(order), ())...)
     else
         _sortdims(tail(tosort), order, (rejected..., tosort[1]))
@@ -32,8 +32,37 @@ const UnionAllTupleOrVector = Union{Vector{UnionAll},Tuple{UnionAll,Vararg}}
 @inline _sortdims(tosort::Tuple, order::Tuple{}, rejected) = ()
 @inline _sortdims(tosort::Tuple{}, order::Tuple{}, rejected) = ()
 
-@inline _dimsmatch(dim::DimOrDimType, match::DimOrDimType) =
+"""
+    commondims(x, lookup)
+
+This is basically `dims` where the order of the original is kept, 
+unlike `dims` where the lookup tuple determines the order
+"""
+commondims(A::AbstractArray, B::AbstractArray) = commondims(dims(A), dims(B))
+commondims(A::AbstractArray, lookup) = commondims(dims(A), lookup)
+commondims(dims::Tuple, lookup) = commondims(dims, (lookup,))
+commondims(dims::Tuple, lookup::Tuple) = 
+    if hasdim(lookup, dims[1])
+        (dims[1], commondims(tail(dims), lookup)...)
+    else
+        commondims(tail(dims), lookup) 
+    end
+commondims(dims::Tuple{}, lookup::Tuple) = ()
+
+
+"""
+    dimsmatch(dim::DimOrDimType, match::DimOrDimType) => Bool
+
+Compare 2 dimensions are of the same base type, or 
+are at least rotations/transformations of the same type.
+"""
+@inline dimsmatch(dims::Tuple, lookups::Tuple) = 
+    all(map(dimsmatch, dims, lookups))
+@inline dimsmatch(dim::DimOrDimType, match::DimOrDimType) =
     basetypeof(dim) <: basetypeof(match) || basetypeof(dim) <: basetypeof(dims(mode(match)))
+@inline dimsmatch(dim::DimOrDimType, match::Nothing) = false
+@inline dimsmatch(dim::Nothing, match::DimOrDimType) = false
+@inline dimsmatch(dim::Nothing, match::Nothing) = false
 
 """
     dims2indices(dim::Dimension, lookup, [emptyval=Colon()])
@@ -195,7 +224,7 @@ julia> dimnum(A, Z)
 
 # Match dim and lookup, also check if the mode has a transformed dimension that matches
 @inline _dimnum(d::Tuple, lookup::Tuple, rejected, n) =
-    if !(d[1] isa Nothing) && _dimsmatch(d[1], lookup[1])
+    if dimsmatch(d[1], lookup[1])
         # Replace found dim with nothing so it isn't found again but n is still correct
         (n, _dimnum((rejected..., nothing, tail(d)...), tail(lookup), (), 1)...)
     else
@@ -234,7 +263,7 @@ false
 @inline hasdim(A::AbstractArray, lookup) = hasdim(dims(A), lookup)
 @inline hasdim(d::Tuple, lookup::Tuple) = map(l -> hasdim(d, l), lookup)
 @inline hasdim(d::Tuple, lookup::DimOrDimType) =
-    if _dimsmatch(d[1], lookup)
+    if dimsmatch(d[1], lookup)
         true
     else
         hasdim(tail(d), lookup)
@@ -242,10 +271,46 @@ false
 @inline hasdim(::Tuple{}, ::DimOrDimType) = false
 
 """
-    setdim(x, newdim)
+    otherdims(x, lookup) => Tuple{Vararg{<:Dimension,N}}
+
+## Arguments
+- `x`: any object with a `dims` method, a `Tuple` of `Dimension`.
+- `lookup`: Tuple or single `Dimension` or dimension `Type`.
+
+A tuple holding the unmatched dimensions is always returned.
+
+## Example
+```jldoctest
+julia> A = DimArray(ones(10, 10, 10), (X, Y, Z));
+
+julia> otherdims(A, X)
+(Y: Base.OneTo(10), Z: Base.OneTo(10))
+
+julia> otherdims(A, Ti)
+(X: Base.OneTo(10), Y: Base.OneTo(10), Z: Base.OneTo(10))
+```
+"""
+@inline otherdims(A::AbstractArray, lookup) = otherdims(dims(A), lookup)
+@inline otherdims(dims::Tuple, lookup::DimOrDimType) = otherdims(dims, (lookup,))
+@inline otherdims(dims::Tuple, lookup::Tuple) =
+    _otherdims(dims, _sortdims(lookup, dims))
+
+#= Work with a sorted lookup where the missing dims are `nothing`.
+Then we can compare with `dimsmatch`, and splat away the matches. =#
+@inline _otherdims(dims::Tuple, sortedlookup::Tuple) =
+    (_otherdims(dims[1], sortedlookup[1])..., 
+     _otherdims(tail(dims), tail(sortedlookup))...)
+@inline _otherdims(dims::Tuple{}, ::Tuple{}) = ()
+@inline _otherdims(dim::DimOrDimType, lookupdim) =
+    dimsmatch(dim, lookupdim) ? () : (dim,)
+
+"""
+    setdims(A::AbstractArray, newdims) => AbstractArray
+    setdims(::Tuple, newdims) => Tuple{Vararg{<:Dimension,N}}
+    setdims(dim::Dimension, newdims) => Dimension
 
-Replaces the first dim matching `<: basetypeof(newdim)` with newdim, and returns
-a new object or tuple with the dimension updated.
+Replaces the first dim matching `<: basetypeof(newdim)` with newdim, 
+and returns a new object or tuple with the dimension updated.
 
 ## Arguments
 - `x`: any object with a `dims` method, a `Tuple` of `Dimension` or a single `Dimension`.
@@ -407,7 +472,7 @@ type: Z{Base.OneTo{Int64},NoIndex,Nothing}
 @inline dims(d::DimTuple, lookup::Tuple) = _dims(d, lookup, (), d)
 
 @inline _dims(d, lookup::Tuple, rejected, remaining) =
-    if !(remaining[1] isa Nothing) && _dimsmatch(remaining[1], lookup[1])
+    if dimsmatch(remaining[1], lookup[1])
         # Remove found dim so it isn't found again
         (remaining[1], _dims(d, tail(lookup), (), (rejected..., tail(remaining)...))...)
     else
diff --git a/src/utils.jl b/src/utils.jl
index a95c08286..78f739b3d 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -134,6 +134,77 @@ modify(f, A::AbstractDimArray) = begin
 end
 
 
+"""
+    dimwise!(f, A::AbstractDimArray, B::AbstractDimArray)
+
+Dimension-wise application of function `f`. 
+
+## Arguments
+
+-`a`: `AbstractDimArray` to broacast from, along dimensions not in `b`.
+-`b`: `AbstractDimArray` to broadcast from all diensions. 
+  Dimensions must be a subset of a.
+
+This is like broadcasting over every slice of `A` if it is 
+sliced by the dimensions of `B`, and storing the value in `dest`.
+"""
+dimwise(f, A::AbstractDimArray, B::AbstractDimArray) = 
+    dimwise!(f, similar(A, promote_type(eltype(A), eltype(B))), A, B)
+
+"""
+    dimwise!(f, dest::AbstractDimArray, A::AbstractDimArray, B::AbstractDimArray)
+
+Dimension-wise application of function `f`. 
+
+## Arguments
+
+-`dest`: `AbstractDimArray` to update
+-`a`: `AbstractDimArray` to broacast from, along dimensions not in `b`.
+-`b`: `AbstractDimArray` to broadcast from all diensions. 
+  Dimensions must be a subset of a.
+
+This is like broadcasting over every slice of `A` if it is 
+sliced by the dimensions of `B`, and storing the value in `dest`.
+"""
+dimwise!(f, dest::AbstractDimArray{T,N}, a::AbstractDimArray{TA,N}, b::AbstractDimArray{TB,NB}
+        ) where {T,TA,TB,N,NB} = begin
+    N >= NB || error("B-array cannot have more dimensions than A array")
+    comparedims(dest, a)
+    common = commondims(a, dims(b))
+    generators = dimwise_generators(otherdims(a, common))
+    # Lazily permute B dims to match the order in A, if required
+    if !dimsmatch(common, dims(b))
+        b = PermutedDimsArray(b, common)
+    end
+    map(generators) do otherdims
+        I = (common..., otherdims...)
+        dest[I...] .= f.(a[I...], b[common...])
+    end
+    return dest
+end
+
+dimwise_generators(dims::Tuple{<:Dimension}) =  
+    ((basetypeof(dims[1])(i),) for i in axes(dims[1], 1))
+
+dimwise_generators(dims::Tuple) = begin
+    dim_constructors = map(basetypeof, dims)
+    Base.Generator(
+        Base.Iterators.ProductIterator(map(d -> axes(d, 1), dims)),
+        vals -> map(dim_constructors, vals)
+    )
+end
+
+"""
+    basetypeof(x)
+
+Get the base type of an object - the minimum required to
+define the object without it's fields. By default this is the full
+`UnionAll` for the type. But custom `basetypeof` methods can be
+defined for types with free type parameters.
+
+In DimensionalData this is primariliy used for comparing dimensions,
+where `Dim{:x}` is different from `Dim{:y}`.
+"""
 basetypeof(x) = basetypeof(typeof(x))
 @generated function basetypeof(::Type{T}) where T
     getfield(parentmodule(T), nameof(T))
diff --git a/test/primitives.jl b/test/primitives.jl
index 013cb7bb9..742627f0e 100644
--- a/test/primitives.jl
+++ b/test/primitives.jl
@@ -1,7 +1,7 @@
 using DimensionalData, Test
 
 using DimensionalData: val, basetypeof, slicedims, dims2indices, formatdims, mode,
-      @dim, reducedims, XDim, YDim, ZDim, Forward
+      @dim, reducedims, XDim, YDim, ZDim, Forward, commondims
 
 dimz = (X(), Y())
 
@@ -138,6 +138,13 @@ end
     @test dims(x) == x
 end
 
+@testset "commondims" begin
+    commondims(da, X) == (dims(da, X),)
+    # Dims are always in the base order
+    commondims(da, (X, Y)) == dims(da, (X, Y))
+    commondims(da, (Y, X)) == dims(da, (X, Y))
+end
+
 @testset "hasdim" begin
     @test hasdim(da, X) == true
     @test hasdim(da, Ti) == false
@@ -153,6 +160,15 @@ end
     @test hasdim(dims(da), (ZDim, ZDim)) == (false, false)
 end
 
+@testset "otherdims" begin
+    A = DimArray(ones(5, 10, 15), (X, Y, Z));
+    @test otherdims(A, X) == dims(A, (Y, Z))
+    @test otherdims(A, Y) == dims(A, (X, Z))
+    @test otherdims(A, Z) == dims(A, (X, Y))
+    @test otherdims(A, (X, Z)) == dims(A, (Y,))
+    @test otherdims(A, Ti) == dims(A, (X, Y, Z))
+end
+
 @testset "setdims" begin
     A = setdims(da, X(LinRange(150,152,2)))
     @test val(dims(dims(A), X())) == LinRange(150,152,2)
diff --git a/test/runtests.jl b/test/runtests.jl
index ce8e0066c..c45f39a5b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -6,8 +6,9 @@ if VERSION >= v"1.5.0"
     Aqua.test_stale_deps(DimensionalData)
 end
 
-include("matmul.jl")
 include("methods.jl")
+include("utils.jl")
+include("matmul.jl")
 include("dimension.jl")
 include("interface.jl")
 include("primitives.jl")
diff --git a/test/utils.jl b/test/utils.jl
index 2542c2552..48c90fb3b 100644
--- a/test/utils.jl
+++ b/test/utils.jl
@@ -67,3 +67,25 @@ end
     typeof(parent(mda)) == BitArray{2}
     @test_throws ErrorException modify(A -> A[1, :], da)
 end
+
+@testset "dimwise" begin
+    A2 = [1 2 3; 4 5 6]
+    B1 = [1, 2, 3]
+    da2 = DimArray(A2, (X, Y))
+    db1 = DimArray(B1, (Y,))
+    dc2 = dimwise(+, da2, db1)
+    @test dc2 == [2 4 6; 5 7 9]
+
+    A3 = cat([1 2 3; 4 5 6], [11 12 13; 14 15 16]; dims=3)
+    da3 = DimArray(A3, (X, Y, Z))
+    db2 = DimArray(A2, (X, Y))
+    dc3 = dimwise(+, da3, db2)
+    @test dc3 == cat([2 4 6; 8 10 12], [12 14 16; 18 20 22]; dims=3)
+
+    @testset "works with permuted dims" begin
+        db2p = permutedims(da2)
+        dc3p = dimwise(+, da3, db2p)
+        @test dc3p == cat([2 4 6; 8 10 12], [12 14 16; 18 20 22]; dims=3)
+    end
+
+end