diff --git a/crates/red_knot_python_semantic/resources/mdtest/comparison/instances/membership_test.md b/crates/red_knot_python_semantic/resources/mdtest/comparison/instances/membership_test.md
new file mode 100644
index 0000000000..21595db3f5
--- /dev/null
+++ b/crates/red_knot_python_semantic/resources/mdtest/comparison/instances/membership_test.md
@@ -0,0 +1,165 @@
+# Comparison: Membership Test
+
+In Python, the term "membership test operators" refers to the operators
+`in` and `not in`. To customize their behavior, classes can implement one of
+the special methods `__contains__`, `__iter__`, or `__getitem__`.
+
+For references, see:
+
+- <https://docs.python.org/3/reference/expressions.html#membership-test-details>
+- <https://docs.python.org/3/reference/datamodel.html#object.__contains__>
+- <https://snarky.ca/unravelling-membership-testing/>
+
+## Implements `__contains__`
+
+Classes can support membership tests by implementing the `__contains__` method:
+
+```py
+class A:
+    def __contains__(self, item: str) -> bool:
+        return True
+
+reveal_type("hello" in A())  # revealed: bool
+reveal_type("hello" not in A())  # revealed: bool
+# TODO: should emit diagnostic, need to check arg type, will fail
+reveal_type(42 in A())  # revealed: bool
+reveal_type(42 not in A())  # revealed: bool
+```
+
+## Implements `__iter__`
+
+Classes that don't implement `__contains__`, but do implement `__iter__`, also
+support containment checks; the needle will be sought in their iterated items:
+
+```py
+class StringIterator:
+    def __next__(self) -> str:
+        return "foo"
+
+class A:
+    def __iter__(self) -> StringIterator:
+        return StringIterator()
+
+reveal_type("hello" in A())  # revealed: bool
+reveal_type("hello" not in A())  # revealed: bool
+reveal_type(42 in A())  # revealed: bool
+reveal_type(42 not in A())  # revealed: bool
+```
+
+## Implements `__getitems__`
+
+The final fallback is to implement `__getitem__` for integer keys. Python will
+call `__getitem__` with `0`, `1`, `2`... until either the needle is found
+(leading the membership test to evaluate to `True`) or `__getitem__` raises
+`IndexError` (the raised exception is swallowed, but results in the membership
+test evaluating to `False`).
+
+```py
+class A:
+    def __getitem__(self, key: int) -> str:
+        return "foo"
+
+reveal_type("hello" in A())  # revealed: bool
+reveal_type("hello" not in A())  # revealed: bool
+reveal_type(42 in A())  # revealed: bool
+reveal_type(42 not in A())  # revealed: bool
+```
+
+## Wrong Return Type
+
+Python coerces the results of containment checks to `bool`, even if `__contains__`
+returns a non-bool:
+
+```py
+class A:
+    def __contains__(self, item: str) -> str:
+        return "foo"
+
+reveal_type("hello" in A())  # revealed: bool
+reveal_type("hello" not in A())  # revealed: bool
+```
+
+## Literal Result for `in` and `not in`
+
+`__contains__` with a literal return type may result in a `BooleanLiteral`
+outcome.
+
+```py
+from typing import Literal
+
+class AlwaysTrue:
+    def __contains__(self, item: int) -> Literal[1]:
+        return 1
+
+class AlwaysFalse:
+    def __contains__(self, item: int) -> Literal[""]:
+        return ""
+
+# TODO: it should be Literal[True] and Literal[False]
+reveal_type(42 in AlwaysTrue())  # revealed: @Todo
+reveal_type(42 not in AlwaysTrue())  # revealed: @Todo
+
+# TODO: it should be Literal[False] and Literal[True]
+reveal_type(42 in AlwaysFalse())  # revealed: @Todo
+reveal_type(42 not in AlwaysFalse())  # revealed: @Todo
+```
+
+## No Fallback for `__contains__`
+
+If `__contains__` is implemented, checking membership of a type it doesn't
+accept is an error; it doesn't result in a fallback to `__iter__` or
+`__getitem__`:
+
+```py
+class CheckContains: ...
+class CheckIter: ...
+class CheckGetItem: ...
+
+class CheckIterIterator:
+    def __next__(self) -> CheckIter:
+        return CheckIter()
+
+class A:
+    def __contains__(self, item: CheckContains) -> bool:
+        return True
+
+    def __iter__(self) -> CheckIterIterator:
+        return CheckIterIterator()
+
+    def __getitem__(self, key: int) -> CheckGetItem:
+        return CheckGetItem()
+
+reveal_type(CheckContains() in A())  # revealed: bool
+
+# TODO: should emit diagnostic, need to check arg type,
+# should not fall back to __iter__ or __getitem__
+reveal_type(CheckIter() in A())  # revealed: bool
+reveal_type(CheckGetItem() in A())  # revealed: bool
+
+class B:
+    def __iter__(self) -> CheckIterIterator:
+        return CheckIterIterator()
+
+    def __getitem__(self, key: int) -> CheckGetItem:
+        return CheckGetItem()
+
+reveal_type(CheckIter() in B())  # revealed: bool
+# Always use `__iter__`, regardless of iterated type; there's no NotImplemented
+# in this case, so there's no fallback to `__getitem__`
+reveal_type(CheckGetItem() in B())  # revealed: bool
+```
+
+## Invalid Old-Style Iteration
+
+If `__getitem__` is implemented but does not accept integer arguments, then
+the membership test is not supported and should trigger a diagnostic.
+
+```py
+class A:
+    def __getitem__(self, key: str) -> str:
+        return "foo"
+
+# TODO should emit a diagnostic
+reveal_type(42 in A())  # revealed: bool
+reveal_type("hello" in A())  # revealed: bool
+```
diff --git a/crates/red_knot_python_semantic/resources/mdtest/comparison/instances/rich_comparison.md b/crates/red_knot_python_semantic/resources/mdtest/comparison/instances/rich_comparison.md
new file mode 100644
index 0000000000..db47ac9ae9
--- /dev/null
+++ b/crates/red_knot_python_semantic/resources/mdtest/comparison/instances/rich_comparison.md
@@ -0,0 +1,336 @@
+# Comparison: Rich Comparison
+
+Rich comparison operations (`==`, `!=`, `<`, `<=`, `>`, `>=`) in Python are
+implemented through double-underscore methods that allow customization of
+comparison behavior.
+
+For references, see:
+
+- <https://docs.python.org/3/reference/datamodel.html#object.__lt__>
+- <https://snarky.ca/unravelling-rich-comparison-operators/>
+
+## Rich Comparison Dunder Implementations For Same Class
+
+Classes can support rich comparison by implementing dunder methods like
+`__eq__`, `__ne__`, etc. The most common case involves implementing these
+methods for the same type:
+
+```py
+from __future__ import annotations
+
+class A:
+    def __eq__(self, other: A) -> int:
+        return 42
+
+    def __ne__(self, other: A) -> float:
+        return 42.0
+
+    def __lt__(self, other: A) -> str:
+        return "42"
+
+    def __le__(self, other: A) -> bytes:
+        return b"42"
+
+    def __gt__(self, other: A) -> list:
+        return [42]
+
+    def __ge__(self, other: A) -> set:
+        return {42}
+
+reveal_type(A() == A())  # revealed: int
+reveal_type(A() != A())  # revealed: float
+reveal_type(A() < A())  # revealed: str
+reveal_type(A() <= A())  # revealed: bytes
+reveal_type(A() > A())  # revealed: list
+reveal_type(A() >= A())  # revealed: set
+```
+
+## Rich Comparison Dunder Implementations for Other Class
+
+In some cases, classes may implement rich comparison dunder methods for
+comparisons with a different type:
+
+```py
+from __future__ import annotations
+
+class A:
+    def __eq__(self, other: B) -> int:
+        return 42
+
+    def __ne__(self, other: B) -> float:
+        return 42.0
+
+    def __lt__(self, other: B) -> str:
+        return "42"
+
+    def __le__(self, other: B) -> bytes:
+        return b"42"
+
+    def __gt__(self, other: B) -> list:
+        return [42]
+
+    def __ge__(self, other: B) -> set:
+        return {42}
+
+class B: ...
+
+reveal_type(A() == B())  # revealed: int
+reveal_type(A() != B())  # revealed: float
+reveal_type(A() < B())  # revealed: str
+reveal_type(A() <= B())  # revealed: bytes
+reveal_type(A() > B())  # revealed: list
+reveal_type(A() >= B())  # revealed: set
+```
+
+## Reflected Comparisons
+
+Fallback to the right-hand side’s comparison methods occurs when the left-hand
+side does not define them. Note: class `B` has its own `__eq__` and `__ne__`
+methods to override those of `object`, but these methods will be ignored here
+because they require a mismatched operand type.
+
+```py
+from __future__ import annotations
+
+class A:
+    def __eq__(self, other: B) -> int:
+        return 42
+
+    def __ne__(self, other: B) -> float:
+        return 42.0
+
+    def __lt__(self, other: B) -> str:
+        return "42"
+
+    def __le__(self, other: B) -> bytes:
+        return b"42"
+
+    def __gt__(self, other: B) -> list:
+        return [42]
+
+    def __ge__(self, other: B) -> set:
+        return {42}
+
+class B:
+    # To override builtins.object.__eq__ and builtins.object.__ne__
+    # TODO these should emit an invalid override diagnostic
+    def __eq__(self, other: str) -> B:
+        return B()
+
+    def __ne__(self, other: str) -> B:
+        return B()
+
+# TODO: should be `int` and `float`.
+# Need to check arg type and fall back to `rhs.__eq__` and `rhs.__ne__`.
+#
+# Because `object.__eq__` and `object.__ne__` accept `object` in typeshed,
+# this can only happen with an invalid override of these methods,
+# but we still support it.
+reveal_type(B() == A())  # revealed: B
+reveal_type(B() != A())  # revealed: B
+
+reveal_type(B() < A())  # revealed: list
+reveal_type(B() <= A())  # revealed: set
+
+reveal_type(B() > A())  # revealed: str
+reveal_type(B() >= A())  # revealed: bytes
+
+class C:
+    def __gt__(self, other: C) -> int:
+        return 42
+
+    def __ge__(self, other: C) -> float:
+        return 42.0
+
+reveal_type(C() < C())  # revealed: int
+reveal_type(C() <= C())  # revealed: float
+```
+
+## Reflected Comparisons with Subclasses
+
+When subclasses override comparison methods, these overridden methods take
+precedence over those in the parent class. Class `B` inherits from `A` and
+redefines comparison methods to return types other than `A`.
+
+```py
+from __future__ import annotations
+
+class A:
+    def __eq__(self, other: A) -> A:
+        return A()
+
+    def __ne__(self, other: A) -> A:
+        return A()
+
+    def __lt__(self, other: A) -> A:
+        return A()
+
+    def __le__(self, other: A) -> A:
+        return A()
+
+    def __gt__(self, other: A) -> A:
+        return A()
+
+    def __ge__(self, other: A) -> A:
+        return A()
+
+class B(A):
+    def __eq__(self, other: A) -> int:
+        return 42
+
+    def __ne__(self, other: A) -> float:
+        return 42.0
+
+    def __lt__(self, other: A) -> str:
+        return "42"
+
+    def __le__(self, other: A) -> bytes:
+        return b"42"
+
+    def __gt__(self, other: A) -> list:
+        return [42]
+
+    def __ge__(self, other: A) -> set:
+        return {42}
+
+reveal_type(A() == B())  # revealed: int
+reveal_type(A() != B())  # revealed: float
+
+reveal_type(A() < B())  # revealed: list
+reveal_type(A() <= B())  # revealed: set
+
+reveal_type(A() > B())  # revealed: str
+reveal_type(A() >= B())  # revealed: bytes
+```
+
+## Reflected Comparisons with Subclass But Falls Back to LHS
+
+In the case of a subclass, the right-hand side has priority. However, if the
+overridden dunder method has an mismatched type to operand, the comparison will
+fall back to the left-hand side.
+
+```py
+from __future__ import annotations
+
+class A:
+    def __lt__(self, other: A) -> A:
+        return A()
+
+    def __gt__(self, other: A) -> A:
+        return A()
+
+class B(A):
+    def __lt__(self, other: int) -> B:
+        return B()
+
+    def __gt__(self, other: int) -> B:
+        return B()
+
+# TODO: should be `A`, need to check argument type and fall back to LHS method
+reveal_type(A() < B())  # revealed: B
+reveal_type(A() > B())  # revealed: B
+```
+
+## Operations involving instances of classes inheriting from `Any`
+
+`Any` and `Unknown` represent a set of possible runtime objects, wherein the
+bounds of the set are unknown. Whether the left-hand operand's dunder or the
+right-hand operand's reflected dunder depends on whether the right-hand operand
+is an instance of a class that is a subclass of the left-hand operand's class
+and overrides the reflected dunder. In the following example, because of the
+unknowable nature of `Any`/`Unknown`, we must consider both possibilities:
+`Any`/`Unknown` might resolve to an unknown third class that inherits from `X`
+and overrides `__gt__`; but it also might not. Thus, the correct answer here for
+the `reveal_type` is `int | Unknown`.
+
+(This test is referenced from `mdtest/binary/instances.md`)
+
+```py
+from does_not_exist import Foo  # error: [unresolved-import]
+
+reveal_type(Foo)  # revealed: Unknown
+
+class X:
+    def __lt__(self, other: object) -> int:
+        return 42
+
+class Y(Foo): ...
+
+# TODO: Should be `int | Unknown`; see above discussion.
+reveal_type(X() < Y())  # revealed: int
+```
+
+## Equality and Inequality Fallback
+
+This test confirms that `==` and `!=` comparisons default to identity
+comparisons (`is`, `is not`) when argument types do not match the method
+signature.
+
+Please refer to the
+[docs](https://docs.python.org/3/reference/datamodel.html#object.__eq__)
+
+```py
+from __future__ import annotations
+
+class A:
+    # TODO both these overrides should emit invalid-override diagnostic
+    def __eq__(self, other: int) -> A:
+        return A()
+
+    def __ne__(self, other: int) -> A:
+        return A()
+
+# TODO: it should be `bool`, need to check arg type and fall back to `is` and `is not`
+reveal_type(A() == A())  # revealed: A
+reveal_type(A() != A())  # revealed: A
+```
+
+## Object Comparisons with Typeshed
+
+```py
+class A: ...
+
+reveal_type(A() == object())  # revealed: bool
+reveal_type(A() != object())  # revealed: bool
+reveal_type(object() == A())  # revealed: bool
+reveal_type(object() != A())  # revealed: bool
+
+# error: [operator-unsupported] "Operator `<` is not supported for types `A` and `object`"
+# revealed: Unknown
+reveal_type(A() < object())
+```
+
+## Numbers Comparison with typeshed
+
+```py
+reveal_type(1 == 1.0)  # revealed: bool
+reveal_type(1 != 1.0)  # revealed: bool
+reveal_type(1 < 1.0)  # revealed: bool
+reveal_type(1 <= 1.0)  # revealed: bool
+reveal_type(1 > 1.0)  # revealed: bool
+reveal_type(1 >= 1.0)  # revealed: bool
+
+reveal_type(1 == 2j)  # revealed: bool
+reveal_type(1 != 2j)  # revealed: bool
+
+# TODO: should be Unknown and emit diagnostic,
+# need to check arg type and should be failed
+reveal_type(1 < 2j)  # revealed: bool
+reveal_type(1 <= 2j)  # revealed: bool
+reveal_type(1 > 2j)  # revealed: bool
+reveal_type(1 >= 2j)  # revealed: bool
+
+def bool_instance() -> bool:
+    return True
+
+def int_instance() -> int:
+    return 42
+
+x = bool_instance()
+y = int_instance()
+
+reveal_type(x < y)  # revealed: bool
+reveal_type(y < x)  # revealed: bool
+reveal_type(4.2 < x)  # revealed: bool
+reveal_type(x < 4.2)  # revealed: bool
+```
diff --git a/crates/red_knot_python_semantic/resources/mdtest/comparison/integers.md b/crates/red_knot_python_semantic/resources/mdtest/comparison/integers.md
index b576ce318d..a2092af109 100644
--- a/crates/red_knot_python_semantic/resources/mdtest/comparison/integers.md
+++ b/crates/red_knot_python_semantic/resources/mdtest/comparison/integers.md
@@ -12,7 +12,8 @@ reveal_type(1 is 1)  # revealed: bool
 reveal_type(1 is not 1)  # revealed: bool
 reveal_type(1 is 2)  # revealed: Literal[False]
 reveal_type(1 is not 7)  # revealed: Literal[True]
-reveal_type(1 <= "" and 0 < 1)  # revealed: @Todo | Literal[True]
+# TODO: should be Unknown, and emit diagnostic, once we check call argument types
+reveal_type(1 <= "" and 0 < 1)  # revealed: bool
 ```
 
 ## Integer instance
@@ -22,7 +23,7 @@ reveal_type(1 <= "" and 0 < 1)  # revealed: @Todo | Literal[True]
 def int_instance() -> int:
     return 42
 
-reveal_type(1 == int_instance())  # revealed: @Todo
+reveal_type(1 == int_instance())  # revealed: bool
 reveal_type(9 < int_instance())  # revealed: bool
 reveal_type(int_instance() < int_instance())  # revealed: bool
 ```
diff --git a/crates/red_knot_python_semantic/resources/mdtest/comparison/tuples.md b/crates/red_knot_python_semantic/resources/mdtest/comparison/tuples.md
index c80ee4d601..7d3d789e07 100644
--- a/crates/red_knot_python_semantic/resources/mdtest/comparison/tuples.md
+++ b/crates/red_knot_python_semantic/resources/mdtest/comparison/tuples.md
@@ -65,20 +65,19 @@ def int_instance() -> int:
 a = (bool_instance(),)
 b = (int_instance(),)
 
-# TODO: All @Todo should be `bool`
-reveal_type(a == a)  # revealed: @Todo
-reveal_type(a != a)  # revealed: @Todo
-reveal_type(a < a)  # revealed: @Todo
-reveal_type(a <= a)  # revealed: @Todo
-reveal_type(a > a)  # revealed: @Todo
-reveal_type(a >= a)  # revealed: @Todo
+reveal_type(a == a)  # revealed: bool
+reveal_type(a != a)  # revealed: bool
+reveal_type(a < a)  # revealed: bool
+reveal_type(a <= a)  # revealed: bool
+reveal_type(a > a)  # revealed: bool
+reveal_type(a >= a)  # revealed: bool
 
-reveal_type(a == b)  # revealed: @Todo
-reveal_type(a != b)  # revealed: @Todo
-reveal_type(a < b)  # revealed: @Todo
-reveal_type(a <= b)  # revealed: @Todo
-reveal_type(a > b)  # revealed: @Todo
-reveal_type(a >= b)  # revealed: @Todo
+reveal_type(a == b)  # revealed: bool
+reveal_type(a != b)  # revealed: bool
+reveal_type(a < b)  # revealed: bool
+reveal_type(a <= b)  # revealed: bool
+reveal_type(a > b)  # revealed: bool
+reveal_type(a >= b)  # revealed: bool
 ```
 
 #### Comparison Unsupported
@@ -90,17 +89,17 @@ However, `==` and `!=` are exceptions and can still provide definite results.
 a = (1, 2)
 b = (1, "hello")
 
-# TODO: should be Literal[False]
-reveal_type(a == b)  # revealed: @Todo
+# TODO: should be Literal[False], once we implement (in)equality for mismatched literals
+reveal_type(a == b)  # revealed: bool
 
-# TODO: should be Literal[True]
-reveal_type(a != b)  # revealed: @Todo
+# TODO: should be Literal[True], once we implement (in)equality for mismatched literals
+reveal_type(a != b)  # revealed: bool
 
 # TODO: should be Unknown and add more informative diagnostics
-reveal_type(a < b)  # revealed: @Todo
-reveal_type(a <= b)  # revealed: @Todo
-reveal_type(a > b)  # revealed: @Todo
-reveal_type(a >= b)  # revealed: @Todo
+reveal_type(a < b)  # revealed: bool
+reveal_type(a <= b)  # revealed: bool
+reveal_type(a > b)  # revealed: bool
+reveal_type(a >= b)  # revealed: bool
 ```
 
 However, if the lexicographic comparison completes without reaching a point where str and int are compared,
@@ -146,13 +145,12 @@ class A:
 
 a = (A(), A())
 
-# TODO: All @Todo should be bool
-reveal_type(a == a)  # revealed: @Todo
-reveal_type(a != a)  # revealed: @Todo
-reveal_type(a < a)  # revealed: @Todo
-reveal_type(a <= a)  # revealed: @Todo
-reveal_type(a > a)  # revealed: @Todo
-reveal_type(a >= a)  # revealed: @Todo
+reveal_type(a == a)  # revealed: bool
+reveal_type(a != a)  # revealed: bool
+reveal_type(a < a)  # revealed: bool
+reveal_type(a <= a)  # revealed: bool
+reveal_type(a > a)  # revealed: bool
+reveal_type(a >= a)  # revealed: bool
 ```
 
 ### Membership Test Comparisons
@@ -174,9 +172,8 @@ reveal_type(a not in b)  # revealed: Literal[False]
 reveal_type(a in c)  # revealed: Literal[False]
 reveal_type(a not in c)  # revealed: Literal[True]
 
-# TODO: All @Todo should be bool
-reveal_type(a in d)  # revealed: @Todo
-reveal_type(a not in d)  # revealed: @Todo
+reveal_type(a in d)  # revealed: bool
+reveal_type(a not in d)  # revealed: bool
 ```
 
 ### Identity Comparisons
@@ -191,10 +188,10 @@ c = (1, 2, 3)
 reveal_type(a is (1, 2))  # revealed: bool
 reveal_type(a is not (1, 2))  # revealed: bool
 
-# TODO: Update to Literal[False] once str == int comparison is implemented
-reveal_type(a is b)  # revealed: @Todo
-# TODO: Update to Literal[True] once str == int comparison is implemented
-reveal_type(a is not b)  # revealed: @Todo
+# TODO should be Literal[False] once we implement comparison of mismatched literal types
+reveal_type(a is b)  # revealed: bool
+# TODO should be Literal[True] once we implement comparison of mismatched literal types
+reveal_type(a is not b)  # revealed: bool
 
 reveal_type(a is c)  # revealed: Literal[False]
 reveal_type(a is not c)  # revealed: Literal[True]
diff --git a/crates/red_knot_python_semantic/resources/mdtest/comparison/unsupported.md b/crates/red_knot_python_semantic/resources/mdtest/comparison/unsupported.md
index f073a19dc5..c1f23b1d48 100644
--- a/crates/red_knot_python_semantic/resources/mdtest/comparison/unsupported.md
+++ b/crates/red_knot_python_semantic/resources/mdtest/comparison/unsupported.md
@@ -10,12 +10,16 @@ reveal_type(a)  # revealed: bool
 b = 0 not in 10  # error: "Operator `not in` is not supported for types `Literal[0]` and `Literal[10]`"
 reveal_type(b)  # revealed: bool
 
-c = object() < 5  # error: "Operator `<` is not supported for types `object` and `int`"
-reveal_type(c)  # revealed: Unknown
+# TODO: should error, once operand type check is implemented
+# ("Operator `<` is not supported for types `object` and `int`")
+c = object() < 5
+# TODO: should be Unknown, once operand type check is implemented
+reveal_type(c)  # revealed: bool
 
-# TODO should error, need to check if __lt__ signature is valid for right operand
+# TODO: should error, once operand type check is implemented
+# ("Operator `<` is not supported for types `int` and `object`")
 d = 5 < object()
-# TODO: should be `Unknown`
+# TODO: should be Unknown, once operand type check is implemented
 reveal_type(d)  # revealed: bool
 
 flag = bool_instance()
@@ -27,5 +31,6 @@ reveal_type(e)  # revealed: bool
 # TODO: should error, need to check if __lt__ signature is valid for right operand
 # error may be "Operator `<` is not supported for types `int` and `str`, in comparing `tuple[Literal[1], Literal[2]]` with `tuple[Literal[1], Literal["hello"]]`
 f = (1, 2) < (1, "hello")
-reveal_type(f)  # revealed: @Todo
+# TODO: should be Unknown, once operand type check is implemented
+reveal_type(f)  # revealed: bool
 ```
diff --git a/crates/red_knot_python_semantic/src/types/infer.rs b/crates/red_knot_python_semantic/src/types/infer.rs
index f3c6b10691..e9e1f99a43 100644
--- a/crates/red_knot_python_semantic/src/types/infer.rs
+++ b/crates/red_knot_python_semantic/src/types/infer.rs
@@ -58,7 +58,7 @@ use crate::types::{
 use crate::util::subscript::PythonSubscript;
 use crate::Db;
 
-use super::{KnownClass, UnionBuilder};
+use super::{IterationOutcome, KnownClass, UnionBuilder};
 
 /// Infer all types for a [`ScopeId`], including all definitions and expressions in that scope.
 /// Use when checking a scope, or needing to provide a type for an arbitrary expression in the
@@ -3101,16 +3101,26 @@ impl<'db> TypeInferenceBuilder<'db> {
             }
 
             // Lookup the rich comparison `__dunder__` methods on instances
-            (Type::Instance(left_class_ty), Type::Instance(right_class_ty)) => match op {
-                ast::CmpOp::Lt => perform_rich_comparison(
-                    self.db,
-                    left_class_ty,
-                    right_class_ty,
-                    RichCompareOperator::Lt,
-                ),
-                // TODO: implement mapping from `ast::CmpOp` to rich comparison methods
-                _ => Ok(Type::Todo),
-            },
+            (Type::Instance(left_class), Type::Instance(right_class)) => {
+                let rich_comparison =
+                    |op| perform_rich_comparison(self.db, left_class, right_class, op);
+                let membership_test_comparison =
+                    |op| perform_membership_test_comparison(self.db, left_class, right_class, op);
+                match op {
+                    ast::CmpOp::Eq => rich_comparison(RichCompareOperator::Eq),
+                    ast::CmpOp::NotEq => rich_comparison(RichCompareOperator::Ne),
+                    ast::CmpOp::Lt => rich_comparison(RichCompareOperator::Lt),
+                    ast::CmpOp::LtE => rich_comparison(RichCompareOperator::Le),
+                    ast::CmpOp::Gt => rich_comparison(RichCompareOperator::Gt),
+                    ast::CmpOp::GtE => rich_comparison(RichCompareOperator::Ge),
+                    ast::CmpOp::In => membership_test_comparison(MembershipTestCompareOperator::In),
+                    ast::CmpOp::NotIn => {
+                        membership_test_comparison(MembershipTestCompareOperator::NotIn)
+                    }
+                    ast::CmpOp::Is => Ok(KnownClass::Bool.to_instance(self.db)),
+                    ast::CmpOp::IsNot => Ok(KnownClass::Bool.to_instance(self.db)),
+                }
+            }
             // TODO: handle more types
             _ => match op {
                 ast::CmpOp::Is | ast::CmpOp::IsNot => Ok(KnownClass::Bool.to_instance(self.db)),
@@ -3623,7 +3633,8 @@ impl From<RichCompareOperator> for ast::CmpOp {
 }
 
 impl RichCompareOperator {
-    const fn dunder_name(self) -> &'static str {
+    #[must_use]
+    const fn dunder(self) -> &'static str {
         match self {
             RichCompareOperator::Eq => "__eq__",
             RichCompareOperator::Ne => "__ne__",
@@ -3633,6 +3644,33 @@ impl RichCompareOperator {
             RichCompareOperator::Ge => "__ge__",
         }
     }
+
+    #[must_use]
+    const fn reflect(self) -> Self {
+        match self {
+            RichCompareOperator::Eq => RichCompareOperator::Eq,
+            RichCompareOperator::Ne => RichCompareOperator::Ne,
+            RichCompareOperator::Lt => RichCompareOperator::Gt,
+            RichCompareOperator::Le => RichCompareOperator::Ge,
+            RichCompareOperator::Gt => RichCompareOperator::Lt,
+            RichCompareOperator::Ge => RichCompareOperator::Le,
+        }
+    }
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+enum MembershipTestCompareOperator {
+    In,
+    NotIn,
+}
+
+impl From<MembershipTestCompareOperator> for ast::CmpOp {
+    fn from(value: MembershipTestCompareOperator) -> Self {
+        match value {
+            MembershipTestCompareOperator::In => ast::CmpOp::In,
+            MembershipTestCompareOperator::NotIn => ast::CmpOp::NotIn,
+        }
+    }
 }
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
@@ -3716,41 +3754,99 @@ impl StringPartsCollector {
 
 /// Rich comparison in Python are the operators `==`, `!=`, `<`, `<=`, `>`, and `>=`. Their
 /// behaviour can be edited for classes by implementing corresponding dunder methods.
-/// This function performs rich comparison between two  instances and returns the resulting type.
+/// This function performs rich comparison between two instances and returns the resulting type.
 /// see `<https://docs.python.org/3/reference/datamodel.html#object.__lt__>`
 fn perform_rich_comparison<'db>(
     db: &'db dyn Db,
-    left: ClassType<'db>,
-    right: ClassType<'db>,
+    left_class: ClassType<'db>,
+    right_class: ClassType<'db>,
     op: RichCompareOperator,
 ) -> Result<Type<'db>, CompareUnsupportedError<'db>> {
     // The following resource has details about the rich comparison algorithm:
     // https://snarky.ca/unravelling-rich-comparison-operators/
     //
-    // TODO: the reflected dunder actually has priority if the r.h.s. is a strict subclass of the
-    // l.h.s.
-    // TODO: `object.__ne__` will call `__eq__` if `__ne__` is not defined
+    // TODO: this currently gives the return type even if the arg types are invalid
+    // (e.g. int.__lt__ with string instance should be errored, currently bool)
 
-    let dunder = left.class_member(db, op.dunder_name());
-    if !dunder.is_unbound() {
-        // TODO: this currently gives the return type even if the arg types are invalid
-        // (e.g. int.__lt__ with string instance should be None, currently bool)
-        return dunder
-            .call(db, &[Type::Instance(left), Type::Instance(right)])
-            .return_ty(db)
-            .ok_or_else(|| CompareUnsupportedError {
-                op: op.into(),
-                left_ty: Type::Instance(left),
-                right_ty: Type::Instance(right),
-            });
+    let call_dunder =
+        |op: RichCompareOperator, left_class: ClassType<'db>, right_class: ClassType<'db>| {
+            left_class
+                .class_member(db, op.dunder())
+                .call(
+                    db,
+                    &[Type::Instance(left_class), Type::Instance(right_class)],
+                )
+                .return_ty(db)
+        };
+
+    // The reflected dunder has priority if the right-hand side is a strict subclass of the left-hand side.
+    if left_class != right_class && right_class.is_subclass_of(db, left_class) {
+        call_dunder(op.reflect(), right_class, left_class)
+            .or_else(|| call_dunder(op, left_class, right_class))
+    } else {
+        call_dunder(op, left_class, right_class)
+            .or_else(|| call_dunder(op.reflect(), right_class, left_class))
     }
-
-    // TODO: reflected dunder -- (==, ==), (!=, !=), (<, >), (>, <), (<=, >=), (>=, <=)
-    Err(CompareUnsupportedError {
-        op: op.into(),
-        left_ty: Type::Instance(left),
-        right_ty: Type::Instance(right),
+    .or_else(|| {
+        // When no appropriate method returns any value other than NotImplemented,
+        // the `==` and `!=` operators will fall back to `is` and `is not`, respectively.
+        // refer to `<https://docs.python.org/3/reference/datamodel.html#object.__eq__>`
+        if matches!(op, RichCompareOperator::Eq | RichCompareOperator::Ne) {
+            Some(KnownClass::Bool.to_instance(db))
+        } else {
+            None
+        }
     })
+    .ok_or_else(|| CompareUnsupportedError {
+        op: op.into(),
+        left_ty: Type::Instance(left_class),
+        right_ty: Type::Instance(right_class),
+    })
+}
+
+/// Performs a membership test (`in` and `not in`) between two instances and returns the resulting type, or `None` if the test is unsupported.
+/// The behavior can be customized in Python by implementing `__contains__`, `__iter__`, or `__getitem__` methods.
+/// See `<https://docs.python.org/3/reference/datamodel.html#object.__contains__>`
+/// and `<https://docs.python.org/3/reference/expressions.html#membership-test-details>`
+fn perform_membership_test_comparison<'db>(
+    db: &'db dyn Db,
+    left_class: ClassType<'db>,
+    right_class: ClassType<'db>,
+    op: MembershipTestCompareOperator,
+) -> Result<Type<'db>, CompareUnsupportedError<'db>> {
+    let (left_instance, right_instance) = (Type::Instance(left_class), Type::Instance(right_class));
+
+    let contains_dunder = right_class.class_member(db, "__contains__");
+
+    let compare_result_opt = if contains_dunder.is_unbound() {
+        // iteration-based membership test
+        match right_instance.iterate(db) {
+            IterationOutcome::Iterable { .. } => Some(KnownClass::Bool.to_instance(db)),
+            IterationOutcome::NotIterable { .. } => None,
+        }
+    } else {
+        // If `__contains__` is available, it is used directly for the membership test.
+        contains_dunder
+            .call(db, &[right_instance, left_instance])
+            .return_ty(db)
+    };
+
+    compare_result_opt
+        .map(|ty| {
+            if matches!(ty, Type::Todo) {
+                return Type::Todo;
+            }
+
+            match op {
+                MembershipTestCompareOperator::In => ty.bool(db).into_type(db),
+                MembershipTestCompareOperator::NotIn => ty.bool(db).negate().into_type(db),
+            }
+        })
+        .ok_or_else(|| CompareUnsupportedError {
+            op: op.into(),
+            left_ty: left_instance,
+            right_ty: right_instance,
+        })
 }
 
 #[cfg(test)]