diff --git a/NEWS.md b/NEWS.md
index 139c9238de7f1..a28b48b0e35be 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -23,6 +23,7 @@ New library functions
 
 New library features
 --------------------
+* Function composition now works also on one argument `∘(f) = f` (#34251)
 
 
 Standard library changes
diff --git a/base/operators.jl b/base/operators.jl
index 049fdf3410273..cd673f791e527 100644
--- a/base/operators.jl
+++ b/base/operators.jl
@@ -837,6 +837,9 @@ and splatting `∘(fs...)` for composing an iterable collection of functions.
 !!! compat "Julia 1.4"
     Multiple function composition requires at least Julia 1.4.
 
+!!! compat "Julia 1.5"
+    Composition of one function ∘(f)  requires at least Julia 1.5.
+
 # Examples
 ```jldoctest
 julia> map(uppercase∘first, ["apple", "banana", "carrot"])
@@ -856,6 +859,8 @@ julia> ∘(fs...)(3)
 3.0
 ```
 """
+function ∘ end
+∘(f) = f
 ∘(f, g) = (x...)->f(g(x...))
 ∘(f, g, h...) = ∘(f ∘ g, h...)
 
diff --git a/test/operators.jl b/test/operators.jl
index 58102d7d65a32..64c0ebab5ab37 100644
--- a/test/operators.jl
+++ b/test/operators.jl
@@ -111,7 +111,30 @@ Base.promote_rule(::Type{T19714}, ::Type{Int}) = T19714
     @test ∘(x -> x-2, x -> x-3, x -> x+5)(7) == 7
     fs = [x -> x[1:2], uppercase, lowercase]
     @test ∘(fs...)("ABC") == "AB"
+
+    # Like +() and *() we leave ∘() undefined.
+    # While `∘() = identity` is a reasonable definition for functions, this
+    # would cause headaches for composition of user defined morphisms.
+    # See also #34251
+    @test_throws(MethodError, ∘())
+
+    @test ∘(x -> (x, 1))(0) === (0, 1)
+    @test ∘(x -> (x, 2), x -> (x, 1))(0) === ((0, 1), 2)
+    @test ∘(x -> (x, 3), x -> (x, 2), x->(x,1))(0) === (((0, 1), 2), 3)
+    @test ∘(x -> (x, 4), x -> (x, 3), x->(x,2), x-> (x, 1))(0) === ((((0, 1), 2), 3), 4)
+
+    # test that user defined functors only need to overload the two arg version
+    struct FreeMagma
+        word
+    end
+    Base.:(∘)(a::FreeMagma, b::FreeMagma) = FreeMagma((a.word, b.word))
+
+    @test ∘(FreeMagma(1)) === FreeMagma(1)
+    @test ∘(FreeMagma(1), FreeMagma(2)) === FreeMagma((1,2))
+    @test ∘(FreeMagma(1), FreeMagma(2), FreeMagma(3)) === FreeMagma(((1,2), 3))
+    @test ∘(FreeMagma(1), FreeMagma(2), FreeMagma(3), FreeMagma(4)) === FreeMagma((((1,2), 3), 4))
 end
+
 @testset "function negation" begin
     str = randstring(20)
     @test filter(!isuppercase, str) == replace(str, r"[A-Z]" => "")