diff --git a/Project.toml b/Project.toml
index 8d7f6fe85..bb1dfe177 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.38.0"
+version = "1.39.0"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/rulesets/Base/base.jl b/src/rulesets/Base/base.jl
index ac712e965..6bea6e06c 100644
--- a/src/rulesets/Base/base.jl
+++ b/src/rulesets/Base/base.jl
@@ -200,3 +200,44 @@ function rrule(::typeof(Base.literal_pow), ::typeof(^), x::Real, ::Val{3})
     cube_pullback(dy) = (NoTangent(), NoTangent(), ProjectTo(x)(3 * x2 * dy), NoTangent())
     return x2 * x, cube_pullback
 end
+
+#####
+##### `map`
+#####
+
+# Ideally reverse mode should always iterate in reverse order. For `map` and broadcasting
+# this may matter with a stateful `f`, but in general their order isn't guaranteed anyway,
+# so it's unclear how much effort should be spent on that. But `map` on Tuples normally
+# gets unrolled, so perhaps it does guarantee order, and reversing it should be cheap too.
+
+function rrule(config::RuleConfig{>:HasReverseMode}, ::typeof(map), f::F, xs::Tuple...) where {F}
+    length_y = minimum(length, xs)
+    hobbits = ntuple(length_y) do i
+        args = getindex.(xs, i)
+        rrule_via_ad(config, f, args...)
+    end
+    y = map(first, hobbits)
+    num_xs = Val(length(xs))
+    paddings = map(x -> ntuple(Returns(NoTangent()), (length(x) - length_y)), xs)
+    all(isempty, paddings) || @error """map(f, xs::Tuple...) does not allow mistmatched lengths!
+        But its `rrule` does; when JuliaLang/julia #42216 is fixed this warning should be removed."""
+    function map_pullback(dy_raw)
+        dy = unthunk(dy_raw)
+        # We want to call the pullbacks in `rrule_via_ad` in reverse sequence to the forward pass:
+        backevals = ntuple(length_y) do i
+            rev_i = length_y - i + 1
+            last(hobbits[rev_i])(dy[rev_i])
+        end |> reverse
+        # This df doesn't infer, could test Base.issingletontype(F), but it's not the only inference problem.
+        df = ProjectTo(f)(sum(first, backevals))
+        # Now unzip that. Because `map` like `zip` should when any `x` stops, some `dx`s may need padding.
+        # Although in fact, `map(+, (1,2), (3,4,5))` is an error... https://github.com/JuliaLang/julia/issues/42216
+        dxs = ntuple(num_xs) do k
+            dx_short = map(bv -> bv[k+1], backevals)
+            ProjectTo(xs[k])((dx_short..., paddings[k]...))  # ProjectTo makes the Tangent for us
+        end
+        return (NoTangent(), df, dxs...)
+    end
+    map_back(dy::AbstractZero) = (NoTangent(), NoTangent(), ntuple(Returns(NoTangent()), num_xs)...)
+    return y, map_pullback
+end
diff --git a/src/rulesets/Base/mapreduce.jl b/src/rulesets/Base/mapreduce.jl
index 1c842feab..a83f72cc7 100644
--- a/src/rulesets/Base/mapreduce.jl
+++ b/src/rulesets/Base/mapreduce.jl
@@ -62,6 +62,17 @@ end
 ##### `sum(f, x)`
 #####
 
+function rrule(config::RuleConfig{>:HasReverseMode}, ::typeof(sum), f::F, xs::Tuple) where {F}
+    fxs, unmap = rrule(config, map, f, xs)
+    y, unsum = rrule(config, sum, fxs)
+    function sum_pullback_f(dy)
+        _, dfxs = unsum(dy)
+        _, df, dxs = unmap(dfxs)
+        (NoTangent(), df, dxs)
+    end
+    y, sum_pullback_f
+end
+
 function rrule(
     config::RuleConfig{>:HasReverseMode},
     ::typeof(sum),
diff --git a/test/rulesets/Base/base.jl b/test/rulesets/Base/base.jl
index 77dff1827..a65881747 100644
--- a/test/rulesets/Base/base.jl
+++ b/test/rulesets/Base/base.jl
@@ -216,4 +216,16 @@
         @test frule(NoRules, 1.0) === nothing
         @test rrule(NoRules, 1.0) === nothing
     end
+    
+    @testset "map(f, ::Tuple...)" begin
+        test_rrule(map, identity, (1.0, 2.0), check_inferred=false)
+        test_rrule(map, +, (1.0, 2.0), (3.0, 4.0), check_inferred=false)
+        test_rrule(map, make_two_vec, (4.0, 5.0 + 6im), check_inferred=false)
+        test_rrule(map, Multiplier(rand() + im), Tuple(rand(3)), check_inferred=false)
+
+        if try map(+, (1,), (2,3)); true catch e; false end
+            # True when https://github.com/JuliaLang/julia/issues/42216 has been fixed
+            test_rrule(map, Multiplier(4.5), (6.7, 8.9), (0.1, 0.2, 0.3), check_inferred=false)
+        end
+    end
 end
diff --git a/test/rulesets/Base/mapreduce.jl b/test/rulesets/Base/mapreduce.jl
index fdbda0a4a..23c4d6da5 100644
--- a/test/rulesets/Base/mapreduce.jl
+++ b/test/rulesets/Base/mapreduce.jl
@@ -67,6 +67,10 @@ const CFG = ChainRulesTestUtils.ADviaRuleConfig()
         end
     end  # sum abs2
 
+    @testset "sum(f, xs::Tuple)" begin
+        test_rrule(sum, sqrt, Tuple(rand(3)), check_inferred=false)
+    end
+
     @testset "sum(f, xs)" begin
         # This calls back into AD
         test_rrule(sum, abs, [-4.0, 2.0, 2.0])