diff --git a/generic_k8s_webhook/config_parser/entrypoint.py b/generic_k8s_webhook/config_parser/entrypoint.py
index daa853e..9d1f970 100644
--- a/generic_k8s_webhook/config_parser/entrypoint.py
+++ b/generic_k8s_webhook/config_parser/entrypoint.py
@@ -100,12 +100,15 @@ def _parse_v1beta1(self, raw_list_webhook_config: dict) -> list[Webhook]:
                 meta_op_parser=op_parser.MetaOperatorParser(
                     list_op_parser_classes=[
                         op_parser.AndParser,
+                        op_parser.AllParser,
                         op_parser.OrParser,
+                        op_parser.AnyParser,
                         op_parser.EqualParser,
                         op_parser.SumParser,
                         op_parser.NotParser,
                         op_parser.ListParser,
                         op_parser.ForEachParser,
+                        op_parser.MapParser,
                         op_parser.ContainParser,
                         op_parser.ConstParser,
                         op_parser.GetValueParser,
diff --git a/generic_k8s_webhook/config_parser/operator_parser.py b/generic_k8s_webhook/config_parser/operator_parser.py
index e3b5016..2835973 100644
--- a/generic_k8s_webhook/config_parser/operator_parser.py
+++ b/generic_k8s_webhook/config_parser/operator_parser.py
@@ -100,6 +100,10 @@ def get_operator_cls(cls) -> operators.BinaryOp:
 
 
 class AndParser(BinaryOpParser):
+    """
+    Deprecated. Use "all" instead
+    """
+
     @classmethod
     def get_name(cls) -> str:
         return "and"
@@ -109,7 +113,21 @@ def get_operator_cls(cls) -> operators.BinaryOp:
         return operators.And
 
 
+class AllParser(AndParser):
+    """
+    Just an alias for "and". In the future, we'll deprecate "and" in favour of "all"
+    """
+
+    @classmethod
+    def get_name(cls) -> str:
+        return "all"
+
+
 class OrParser(BinaryOpParser):
+    """
+    Deprecated. Use "any" instead
+    """
+
     @classmethod
     def get_name(cls) -> str:
         return "or"
@@ -119,6 +137,16 @@ def get_operator_cls(cls) -> operators.BinaryOp:
         return operators.Or
 
 
+class AnyParser(OrParser):
+    """
+    Just an alias for "or". In the future, we'll deprecate "or" in favour of "all"
+    """
+
+    @classmethod
+    def get_name(cls) -> str:
+        return "any"
+
+
 class EqualParser(BinaryOpParser):
     @classmethod
     def get_name(cls) -> str:
@@ -180,6 +208,10 @@ def parse(self, op_inputs: dict | list, path_op: str) -> operators.List:
 
 
 class ForEachParser(OperatorParser):
+    """
+    Deprecated. Use "map" instead of "forEach"
+    """
+
     @classmethod
     def get_name(cls) -> str:
         return "forEach"
@@ -197,6 +229,16 @@ def parse(self, op_inputs: dict | list, path_op: str) -> operators.ForEach:
             raise ParsingException(f"Error when parsing {path_op}") from e
 
 
+class MapParser(ForEachParser):
+    """
+    It's an alias of ForEachParser. In the future, we'll deprecate "forEach" in favour of "map"
+    """
+
+    @classmethod
+    def get_name(cls) -> str:
+        return "map"
+
+
 class ContainParser(OperatorParser):
     @classmethod
     def get_name(cls) -> str:
diff --git a/generic_k8s_webhook/operators.py b/generic_k8s_webhook/operators.py
index 437fe72..23f27ec 100644
--- a/generic_k8s_webhook/operators.py
+++ b/generic_k8s_webhook/operators.py
@@ -110,6 +110,7 @@ def _op(self, lhs, rhs):
         return lhs and rhs
 
     def _zero_args_result(self):
+        # This follows the default behaviour in Python when executing `all([])`
         return True
 
 
@@ -118,7 +119,8 @@ def _op(self, lhs, rhs):
         return lhs or rhs
 
     def _zero_args_result(self):
-        return True
+        # This follows the default behaviour in Python when executing `any([])`
+        return False
 
 
 class ArithOp(BinaryOp):
diff --git a/tests/conditions_test.yaml b/tests/conditions_test.yaml
index df3ec52..7d5b87a 100644
--- a/tests/conditions_test.yaml
+++ b/tests/conditions_test.yaml
@@ -31,6 +31,16 @@ test_suites:
           - condition:
               and: []
             expected_result: true
+  # Just check we can parse "all", since it's the same as "and"
+  - name: ALL
+    tests:
+      - schemas: [v1beta1]
+        cases:
+          - condition:
+              all:
+                - const: true
+                - const: true
+            expected_result: true
   - name: OR
     tests:
       - schemas: [v1alpha1]
@@ -49,6 +59,19 @@ test_suites:
               or:
                 - const: true
             expected_result: true
+          - condition:
+              or: []
+            expected_result: false
+  # Just check we can parse "any", since it's the same as "or"
+  - name: ANY
+    tests:
+      - schemas: [v1beta1]
+        cases:
+          - condition:
+              any:
+                - const: false
+                - const: false
+            expected_result: false
   - name: NOT
     tests:
       - schemas: [v1alpha1]
@@ -143,6 +166,20 @@ test_suites:
                   - maxCPU: 1
                   - maxCPU: 2
             expected_result: [2, 3]
+  # Just check we can parse "map", since it's the same as "forEach"
+  - name: MAP
+    tests:
+      - schemas: [v1beta1]
+        cases:
+          - condition:
+              map:
+                elements:
+                  const: [1, 2]
+                op:
+                  sum:
+                    - const: 10
+                    - getValue: "."
+            expected_result: [11, 12]
   - name: CONTAIN
     tests:
       - schemas: [v1alpha1]