diff --git a/airflow/models/xcom_arg.py b/airflow/models/xcom_arg.py
index 2fb60195ef911..9be82976ae2c8 100644
--- a/airflow/models/xcom_arg.py
+++ b/airflow/models/xcom_arg.py
@@ -14,10 +14,12 @@
 # KIND, either express or implied.  See the License for the
 # specific language governing permissions and limitations
 # under the License.
+
 from __future__ import annotations
 
+import contextlib
 import inspect
-from typing import TYPE_CHECKING, Any, Callable, Iterator, Mapping, Sequence, overload
+from typing import TYPE_CHECKING, Any, Callable, Iterator, Mapping, Sequence, Union, overload
 
 from sqlalchemy import func
 from sqlalchemy.orm import Session
@@ -35,6 +37,11 @@
     from airflow.models.dag import DAG
     from airflow.models.operator import Operator
 
+# Callable objects contained by MapXComArg. We only accept callables from
+# the user, but deserialize them into strings in a serialized XComArg for
+# safety (those callables are arbitrary user code).
+MapCallables = Sequence[Union[Callable[[Any], Any], str]]
+
 
 class XComArg(DependencyMixin):
     """Reference to an XCom value pushed from another operator.
@@ -322,15 +329,39 @@ def resolve(self, context: Context, session: Session = NEW_SESSION) -> Any:
         raise XComNotFound(context["ti"].dag_id, task_id, self.key)
 
 
+def _get_callable_name(f: Callable | str) -> str:
+    """Try to "describe" a callable by getting its name."""
+    if callable(f):
+        return f.__name__
+    # Parse the source to find whatever is behind "def". For safety, we don't
+    # want to evaluate the code in any meaningful way!
+    with contextlib.suppress(Exception):
+        kw, name, _ = f.lstrip().split(None, 2)
+        if kw == "def":
+            return name
+    return "<function>"
+
+
 class _MapResult(Sequence):
-    def __init__(self, value: Sequence | dict, callables: Sequence[Callable[[Any], Any]]) -> None:
+    def __init__(self, value: Sequence | dict, callables: MapCallables) -> None:
         self.value = value
         self.callables = callables
 
     def __getitem__(self, index: Any) -> Any:
         value = self.value[index]
-        for f in self.callables:
-            value = f(value)
+
+        # In the worker, we can access all actual callables. Call them.
+        callables = [f for f in self.callables if callable(f)]
+        if len(callables) == len(self.callables):
+            for f in callables:
+                value = f(value)
+            return value
+
+        # In the scheduler, we don't have access to the actual callables, nor do
+        # we want to run it since it's arbitrary code. This builds a string to
+        # represent the call chain in the UI or logs instead.
+        for v in self.callables:
+            value = f"{_get_callable_name(v)}({value})"
         return value
 
     def __len__(self) -> int:
@@ -342,9 +373,11 @@ class MapXComArg(XComArg):
 
     This is based on an XComArg, but also applies a series of "transforms" that
     convert the pulled XCom value.
+
+    :meta private:
     """
 
-    def __init__(self, arg: XComArg, callables: Sequence[Callable[[Any], Any]]) -> None:
+    def __init__(self, arg: XComArg, callables: MapCallables) -> None:
         for c in callables:
             if getattr(c, "_airflow_is_task_decorator", False):
                 raise ValueError("map() argument must be a plain function, not a @task operator")
@@ -352,12 +385,13 @@ def __init__(self, arg: XComArg, callables: Sequence[Callable[[Any], Any]]) -> N
         self.callables = callables
 
     def __repr__(self) -> str:
-        return f"{self.arg!r}.map([{len(self.callables)} functions])"
+        map_calls = "".join(f".map({_get_callable_name(f)})" for f in self.callables)
+        return f"{self.arg!r}{map_calls}"
 
     def _serialize(self) -> dict[str, Any]:
         return {
             "arg": serialize_xcom_arg(self.arg),
-            "callables": [inspect.getsource(c) for c in self.callables],
+            "callables": [inspect.getsource(c) if callable(c) else c for c in self.callables],
         }
 
     @classmethod
diff --git a/tests/models/test_xcom_arg.py b/tests/models/test_xcom_arg.py
index 18cbe87de1f8f..1f9a342c026d1 100644
--- a/tests/models/test_xcom_arg.py
+++ b/tests/models/test_xcom_arg.py
@@ -211,14 +211,14 @@ def pull(value):
 
     # Run "push_letters" and "push_numbers".
     decision = dr.task_instance_scheduling_decisions(session=session)
-    assert decision.schedulable_tis and all(ti.task_id.startswith("push_") for ti in decision.schedulable_tis)
+    assert sorted(ti.task_id for ti in decision.schedulable_tis) == ["push_letters", "push_numbers"]
     for ti in decision.schedulable_tis:
         ti.run(session=session)
     session.commit()
 
     # Run "pull".
     decision = dr.task_instance_scheduling_decisions(session=session)
-    assert decision.schedulable_tis and all(ti.task_id == "pull" for ti in decision.schedulable_tis)
+    assert sorted(ti.task_id for ti in decision.schedulable_tis) == ["pull"] * len(expected_results)
     for ti in decision.schedulable_tis:
         ti.run(session=session)