diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index f72a214f120a0..ca9c16bd6e582 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -4574,36 +4574,44 @@ def query(self, expr: str, *, inplace: bool = False, **kwargs) -> DataFrame | No
         Examples
         --------
         >>> df = pd.DataFrame(
-        ...     {"A": range(1, 6), "B": range(10, 0, -2), "C C": range(10, 5, -1)}
+        ...     {"A": range(1, 6), "B": range(10, 0, -2), "C&C": range(10, 5, -1)}
         ... )
         >>> df
-           A   B  C C
+           A   B  C&C
         0  1  10   10
         1  2   8    9
         2  3   6    8
         3  4   4    7
         4  5   2    6
         >>> df.query("A > B")
-           A  B  C C
+           A  B  C&C
         4  5  2    6
 
         The previous expression is equivalent to
 
         >>> df[df.A > df.B]
-           A  B  C C
+           A  B  C&C
         4  5  2    6
 
         For columns with spaces in their name, you can use backtick quoting.
 
-        >>> df.query("B == `C C`")
-           A   B  C C
+        >>> df.query("B == `C&C`")
+           A   B  C&C
         0  1  10   10
 
         The previous expression is equivalent to
 
-        >>> df[df.B == df["C C"]]
-           A   B  C C
+        >>> df[df.B == df["C&C"]]
+           A   B  C&C
         0  1  10   10
+
+        Using local variable:
+
+        >>> local_var = 2
+        >>> df.query("A <= @local_var")
+        A   B  C&C
+        0  1  10   10
+        1  2   8    9
         """
         inplace = validate_bool_kwarg(inplace, "inplace")
         if not isinstance(expr, str):
@@ -4644,6 +4652,13 @@ def eval(self, expr: str, *, inplace: bool = False, **kwargs) -> Any | None:
         ----------
         expr : str
             The expression string to evaluate.
+
+            You can refer to variables
+            in the environment by prefixing them with an '@' character like
+            ``@a + b``.
+
+            You can refer to column names that are not valid Python variable
+            names by surrounding them with backticks `````.
         inplace : bool, default False
             If the expression contains an assignment, whether to perform the
             operation inplace and mutate the existing DataFrame. Otherwise,
@@ -4675,14 +4690,16 @@ def eval(self, expr: str, *, inplace: bool = False, **kwargs) -> Any | None:
 
         Examples
         --------
-        >>> df = pd.DataFrame({"A": range(1, 6), "B": range(10, 0, -2)})
+        >>> df = pd.DataFrame(
+        ...     {"A": range(1, 6), "B": range(10, 0, -2), "C&C": range(10, 5, -1)}
+        ... )
         >>> df
-           A   B
-        0  1  10
-        1  2   8
-        2  3   6
-        3  4   4
-        4  5   2
+           A   B  C&C
+        0  1  10   10
+        1  2   8    9
+        2  3   6    8
+        3  4   4    7
+        4  5   2    6
         >>> df.eval("A + B")
         0    11
         1    10
@@ -4694,35 +4711,55 @@ def eval(self, expr: str, *, inplace: bool = False, **kwargs) -> Any | None:
         Assignment is allowed though by default the original DataFrame is not
         modified.
 
-        >>> df.eval("C = A + B")
-           A   B   C
-        0  1  10  11
-        1  2   8  10
-        2  3   6   9
-        3  4   4   8
-        4  5   2   7
+        >>> df.eval("D = A + B")
+           A   B  C&C   D
+        0  1  10   10  11
+        1  2   8    9  10
+        2  3   6    8   9
+        3  4   4    7   8
+        4  5   2    6   7
         >>> df
-           A   B
-        0  1  10
-        1  2   8
-        2  3   6
-        3  4   4
-        4  5   2
+           A   B  C&C
+        0  1  10   10
+        1  2   8    9
+        2  3   6    8
+        3  4   4    7
+        4  5   2    6
 
         Multiple columns can be assigned to using multi-line expressions:
 
         >>> df.eval(
         ...     '''
-        ... C = A + B
-        ... D = A - B
+        ... D = A + B
+        ... E = A - B
         ... '''
         ... )
-           A   B   C  D
-        0  1  10  11 -9
-        1  2   8  10 -6
-        2  3   6   9 -3
-        3  4   4   8  0
-        4  5   2   7  3
+           A   B  C&C   D  E
+        0  1  10   10  11 -9
+        1  2   8    9  10 -6
+        2  3   6    8   9 -3
+        3  4   4    7   8  0
+        4  5   2    6   7  3
+
+        For columns with spaces in their name, you can use backtick quoting.
+
+        >>> df.eval("B * `C&C`")
+        0    100
+        1     72
+        2     48
+        3     28
+        4     12
+
+        Local variables shall be explicitly referenced using ``@``
+        character in front of the name:
+
+        >>> local_var = 2
+        >>> df.eval("@local_var * A")
+        0     2
+        1     4
+        2     6
+        3     8
+        4    10
         """
         from pandas.core.computation.eval import eval as _eval