diff --git a/py-polars/polars/expr/expr.py b/py-polars/polars/expr/expr.py
index d5d40217f72d..ec308fa9c28c 100644
--- a/py-polars/polars/expr/expr.py
+++ b/py-polars/polars/expr/expr.py
@@ -4965,7 +4965,7 @@ def limit(self, n: int | Expr = 10) -> Expr:
         """
         return self.head(n)
 
-    def and_(self, *others: Any) -> Expr:
+    def and_(self, *others: IntoExprColumn | int | bool) -> Expr:
         """
         Method equivalent of bitwise "and" operator `expr & other & ...`.
 
@@ -5006,9 +5006,9 @@ def and_(self, *others: Any) -> Expr:
         │ false │
         └───────┘
         """
-        return reduce(operator.and_, (self, *others))
+        return reduce(operator.and_, (self, *others))  # type: ignore[return-value]
 
-    def or_(self, *others: Any) -> Expr:
+    def or_(self, *others: IntoExprColumn | int | bool) -> Expr:
         """
         Method equivalent of bitwise "or" operator `expr | other | ...`.
 
@@ -5048,9 +5048,9 @@ def or_(self, *others: Any) -> Expr:
         │ false │
         └───────┘
         """
-        return reduce(operator.or_, (self,) + others)
+        return reduce(operator.or_, (self,) + others)  # type: ignore[return-value]
 
-    def eq(self, other: Any) -> Expr:
+    def eq(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of equality operator `expr == other`.
 
@@ -5084,7 +5084,7 @@ def eq(self, other: Any) -> Expr:
         """
         return self.__eq__(other)
 
-    def eq_missing(self, other: Any) -> Expr:
+    def eq_missing(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of equality operator `expr == other` where `None == None`.
 
@@ -5124,7 +5124,7 @@ def eq_missing(self, other: Any) -> Expr:
         other = parse_into_expression(other, str_as_lit=True)
         return self._from_pyexpr(self._pyexpr.eq_missing(other))
 
-    def ge(self, other: Any) -> Expr:
+    def ge(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of "greater than or equal" operator `expr >= other`.
 
@@ -5158,7 +5158,7 @@ def ge(self, other: Any) -> Expr:
         """
         return self.__ge__(other)
 
-    def gt(self, other: Any) -> Expr:
+    def gt(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of "greater than" operator `expr > other`.
 
@@ -5192,7 +5192,7 @@ def gt(self, other: Any) -> Expr:
         """
         return self.__gt__(other)
 
-    def le(self, other: Any) -> Expr:
+    def le(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of "less than or equal" operator `expr <= other`.
 
@@ -5226,7 +5226,7 @@ def le(self, other: Any) -> Expr:
         """
         return self.__le__(other)
 
-    def lt(self, other: Any) -> Expr:
+    def lt(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of "less than" operator `expr < other`.
 
@@ -5260,7 +5260,7 @@ def lt(self, other: Any) -> Expr:
         """
         return self.__lt__(other)
 
-    def ne(self, other: Any) -> Expr:
+    def ne(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of inequality operator `expr != other`.
 
@@ -5294,7 +5294,7 @@ def ne(self, other: Any) -> Expr:
         """
         return self.__ne__(other)
 
-    def ne_missing(self, other: Any) -> Expr:
+    def ne_missing(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of equality operator `expr != other` where `None == None`.
 
@@ -5334,7 +5334,7 @@ def ne_missing(self, other: Any) -> Expr:
         other = parse_into_expression(other, str_as_lit=True)
         return self._from_pyexpr(self._pyexpr.neq_missing(other))
 
-    def add(self, other: Any) -> Expr:
+    def add(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of addition operator `expr + other`.
 
@@ -5380,7 +5380,7 @@ def add(self, other: Any) -> Expr:
         """
         return self.__add__(other)
 
-    def floordiv(self, other: Any) -> Expr:
+    def floordiv(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of integer division operator `expr // other`.
 
@@ -5467,7 +5467,7 @@ def floordiv(self, other: Any) -> Expr:
         """
         return self.__floordiv__(other)
 
-    def mod(self, other: Any) -> Expr:
+    def mod(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of modulus operator `expr % other`.
 
@@ -5495,7 +5495,7 @@ def mod(self, other: Any) -> Expr:
         """
         return self.__mod__(other)
 
-    def mul(self, other: Any) -> Expr:
+    def mul(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of multiplication operator `expr * other`.
 
@@ -5526,7 +5526,7 @@ def mul(self, other: Any) -> Expr:
         """
         return self.__mul__(other)
 
-    def sub(self, other: Any) -> Expr:
+    def sub(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of subtraction operator `expr - other`.
 
@@ -5579,7 +5579,7 @@ def neg(self) -> Expr:
         """
         return self.__neg__()
 
-    def truediv(self, other: Any) -> Expr:
+    def truediv(self, other: IntoExpr) -> Expr:
         """
         Method equivalent of float division operator `expr / other`.
 
@@ -5676,7 +5676,7 @@ def pow(self, exponent: IntoExprColumn | int | float) -> Expr:
         """
         return self.__pow__(exponent)
 
-    def xor(self, other: Any) -> Expr:
+    def xor(self, other: IntoExprColumn | int | bool) -> Expr:
         """
         Method equivalent of bitwise exclusive-or operator `expr ^ other`.