diff --git a/mypy/partially_defined.py b/mypy/partially_defined.py
--- a/mypy/partially_defined.py
+++ b/mypy/partially_defined.py
@@ -31,6 +31,7 @@
     RefExpr,
     ReturnStmt,
     StarExpr,
+    TryStmt,
     TupleExpr,
     WhileStmt,
     WithStmt,
@@ -66,6 +67,13 @@ def __init__(
         self.must_be_defined = set(must_be_defined)
         self.skipped = skipped
 
+    def copy(self) -> BranchState:
+        return BranchState(
+            must_be_defined=set(self.must_be_defined),
+            may_be_defined=set(self.may_be_defined),
+            skipped=self.skipped,
+        )
+
 
 class BranchStatement:
     def __init__(self, initial_state: BranchState) -> None:
@@ -77,6 +85,11 @@ def __init__(self, initial_state: BranchState) -> None:
             )
         ]
 
+    def copy(self) -> BranchStatement:
+        result = BranchStatement(self.initial_state)
+        result.branches = [b.copy() for b in self.branches]
+        return result
+
     def next_branch(self) -> None:
         self.branches.append(
             BranchState(
@@ -90,6 +103,11 @@ def record_definition(self, name: str) -> None:
         self.branches[-1].must_be_defined.add(name)
         self.branches[-1].may_be_defined.discard(name)
 
+    def delete_var(self, name: str) -> None:
+        assert len(self.branches) > 0
+        self.branches[-1].must_be_defined.discard(name)
+        self.branches[-1].may_be_defined.discard(name)
+
     def record_nested_branch(self, state: BranchState) -> None:
         assert len(self.branches) > 0
         current_branch = self.branches[-1]
@@ -151,6 +169,11 @@ def __init__(self, stmts: list[BranchStatement]) -> None:
         self.branch_stmts: list[BranchStatement] = stmts
         self.undefined_refs: dict[str, set[NameExpr]] = {}
 
+    def copy(self) -> Scope:
+        result = Scope([s.copy() for s in self.branch_stmts])
+        result.undefined_refs = self.undefined_refs.copy()
+        return result
+
     def record_undefined_ref(self, o: NameExpr) -> None:
         if o.name not in self.undefined_refs:
             self.undefined_refs[o.name] = set()
@@ -166,6 +189,15 @@ class DefinedVariableTracker:
     def __init__(self) -> None:
         # There's always at least one scope. Within each scope, there's at least one "global" BranchingStatement.
         self.scopes: list[Scope] = [Scope([BranchStatement(BranchState())])]
+        # disable_branch_skip is used to disable skipping a branch due to a return/raise/etc. This is useful
+        # in things like try/except/finally statements.
+        self.disable_branch_skip = False
+
+    def copy(self) -> DefinedVariableTracker:
+        result = DefinedVariableTracker()
+        result.scopes = [s.copy() for s in self.scopes]
+        result.disable_branch_skip = self.disable_branch_skip
+        return result
 
     def _scope(self) -> Scope:
         assert len(self.scopes) > 0
@@ -195,7 +227,7 @@ def end_branch_statement(self) -> None:
 
     def skip_branch(self) -> None:
         # Only skip branch if we're outside of "root" branch statement.
-        if len(self._scope().branch_stmts) > 1:
+        if len(self._scope().branch_stmts) > 1 and not self.disable_branch_skip:
             self._scope().branch_stmts[-1].skip_branch()
 
     def record_definition(self, name: str) -> None:
@@ -203,6 +235,11 @@ def record_definition(self, name: str) -> None:
         assert len(self.scopes[-1].branch_stmts) > 0
         self._scope().branch_stmts[-1].record_definition(name)
 
+    def delete_var(self, name: str) -> None:
+        assert len(self.scopes) > 0
+        assert len(self.scopes[-1].branch_stmts) > 0
+        self._scope().branch_stmts[-1].delete_var(name)
+
     def record_undefined_ref(self, o: NameExpr) -> None:
         """Records an undefined reference. These can later be retrieved via `pop_undefined_ref`."""
         assert len(self.scopes) > 0
@@ -268,6 +305,7 @@ def __init__(
         self.type_map = type_map
         self.options = options
         self.loops: list[Loop] = []
+        self.try_depth = 0
         self.tracker = DefinedVariableTracker()
         for name in implicit_module_attrs:
             self.tracker.record_definition(name)
@@ -432,6 +470,75 @@ def visit_expression_stmt(self, o: ExpressionStmt) -> None:
             self.tracker.skip_branch()
         super().visit_expression_stmt(o)
 
+    def visit_try_stmt(self, o: TryStmt) -> None:
+        """
+        Note that finding undefined vars in `finally` requires different handling from
+        the rest of the code. In particular, we want to disallow skipping branches due to jump
+        statements in except/else clauses for finally but not for other cases. Imagine a case like:
+        def f() -> int:
+            try:
+                x = 1
+            except:
+                # This jump statement needs to be handled differently depending on whether or
+                # not we're trying to process `finally` or not.
+                return 0
+            finally:
+                # `x` may be undefined here.
+                pass
+            # `x` is always defined here.
+            return x
+        """
+        self.try_depth += 1
+        if o.finally_body is not None:
+            # In order to find undefined vars in `finally`, we need to
+            # process try/except with branch skipping disabled. However, for the rest of the code
+            # after finally, we need to process try/except with branch skipping enabled.
+            # Therefore, we need to process try/finally twice.
+            # Because processing is not idempotent, we should make a copy of the tracker.
+            old_tracker = self.tracker.copy()
+            self.tracker.disable_branch_skip = True
+            self.process_try_stmt(o)
+            self.tracker = old_tracker
+        self.process_try_stmt(o)
+        self.try_depth -= 1
+
+    def process_try_stmt(self, o: TryStmt) -> None:
+        """
+        Processes try statement decomposing it into the following:
+        if ...:
+            body
+            else_body
+        elif ...:
+            except 1
+        elif ...:
+            except 2
+        else:
+            except n
+        finally
+        """
+        self.tracker.start_branch_statement()
+        o.body.accept(self)
+        if o.else_body is not None:
+            o.else_body.accept(self)
+        if len(o.handlers) > 0:
+            assert len(o.handlers) == len(o.vars) == len(o.types)
+            for i in range(len(o.handlers)):
+                self.tracker.next_branch()
+                exc_type = o.types[i]
+                if exc_type is not None:
+                    exc_type.accept(self)
+                var = o.vars[i]
+                if var is not None:
+                    self.process_definition(var.name)
+                    var.accept(self)
+                o.handlers[i].accept(self)
+                if var is not None:
+                    self.tracker.delete_var(var.name)
+        self.tracker.end_branch_statement()
+
+        if o.finally_body is not None:
+            o.finally_body.accept(self)
+
     def visit_while_stmt(self, o: WhileStmt) -> None:
         o.expr.accept(self)
         self.tracker.start_branch_statement()
@@ -478,7 +585,9 @@ def visit_name_expr(self, o: NameExpr) -> None:
             self.tracker.record_definition(o.name)
         elif self.tracker.is_defined_in_different_branch(o.name):
             # A variable is defined in one branch but used in a different branch.
-            if self.loops:
+            if self.loops or self.try_depth > 0:
+                # If we're in a loop or in a try, we can't be sure that this variable
+                # is undefined. Report it as "may be undefined".
                 self.variable_may_be_undefined(o.name, o)
             else:
                 self.var_used_before_def(o.name, o)

diff --git a/test-data/unit/check-possibly-undefined.test b/test-data/unit/check-possibly-undefined.test
--- a/test-data/unit/check-possibly-undefined.test
+++ b/test-data/unit/check-possibly-undefined.test
@@ -525,6 +525,190 @@ def f3() -> None:
         y = x
     z = x  # E: Name "x" may be undefined
 
+[case testTryBasic]
+# flags: --enable-error-code possibly-undefined --enable-error-code used-before-def
+def f1() -> int:
+    try:
+        x = 1
+    except:
+        pass
+    return x  # E: Name "x" may be undefined
+
+def f2() -> int:
+    try:
+        pass
+    except:
+        x = 1
+    return x  # E: Name "x" may be undefined
+
+def f3() -> int:
+    try:
+        x = 1
+    except:
+        y = x  # E: Name "x" may be undefined
+    return x  # E: Name "x" may be undefined
+
+def f4() -> int:
+    try:
+        x = 1
+    except:
+        return 0
+    return x
+
+def f5() -> int:
+    try:
+        x = 1
+    except:
+        raise
+    return x
+
+def f6() -> None:
+    try:
+        pass
+    except BaseException as exc:
+        x = exc  # No error.
+        exc = BaseException()
+    # This case is covered by the other check, not by possibly undefined check.
+    y = exc # E: Trying to read deleted variable "exc"
+
+def f7() -> int:
+    try:
+        if int():
+            x = 1
+        assert False
+    except:
+        pass
+    return x  # E: Name "x" may be undefined
+[builtins fixtures/exception.pyi]
+
+[case testTryMultiExcept]
+# flags: --enable-error-code possibly-undefined
+def f1() -> int:
+    try:
+        x = 1
+    except BaseException:
+        x = 2
+    except:
+        x = 3
+    return x
+
+def f2() -> int:
+    try:
+        x = 1
+    except BaseException:
+        pass
+    except:
+        x = 3
+    return x  # E: Name "x" may be undefined
+[builtins fixtures/exception.pyi]
+
+[case testTryFinally]
+# flags: --enable-error-code possibly-undefined --enable-error-code used-before-def
+def f1() -> int:
+    try:
+        x = 1
+    finally:
+        x = 2
+    return x
+
+def f2() -> int:
+    try:
+        pass
+    except:
+        pass
+    finally:
+        x = 2
+    return x
+
+def f3() -> int:
+    try:
+        x = 1
+    except:
+        pass
+    finally:
+        y = x  # E: Name "x" may be undefined
+    return x
+
+def f4() -> int:
+    try:
+        x = 0
+    except BaseException:
+        raise
+    finally:
+        y = x  # E: Name "x" may be undefined
+    return y
+
+def f5() -> int:
+    try:
+        if int():
+            x = 1
+        else:
+            return 0
+    finally:
+        pass
+    return x  # No error.
+
+def f6() -> int:
+    try:
+        if int():
+            x = 1
+        else:
+            return 0
+    finally:
+        a = x  # E: Name "x" may be undefined
+    return a
+[builtins fixtures/exception.pyi]
+
+[case testTryElse]
+# flags: --enable-error-code possibly-undefined
+def f1() -> int:
+    try:
+        return 0
+    except BaseException:
+        x = 1
+    else:
+        x = 2
+    finally:
+        y = x
+    return y
+
+def f2() -> int:
+    try:
+        pass
+    except:
+        x = 1
+    else:
+        x = 2
+    return x
+
+def f3() -> int:
+    try:
+        pass
+    except:
+        x = 1
+    else:
+        pass
+    return x  # E: Name "x" may be undefined
+
+def f4() -> int:
+    try:
+        x = 1
+    except:
+        x = 2
+    else:
+        pass
+    return x
+
+def f5() -> int:
+    try:
+        pass
+    except:
+        x = 1
+    else:
+        return 1
+    return x
+[builtins fixtures/exception.pyi]
+
 [case testNoReturn]
 # flags: --enable-error-code possibly-undefined
 

Support try/except in partially defined check
Currently, partially defined check (`--enable-error-code partially-defined`) does not support detecting partially defined variables try/except statement. 

The most basic example is the following:
```python
try:
  x = foo()
except:
  pass
y = x  # mypy should generate an error here but does not.
```

mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testIndexExpr mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testDefinedInOneBranch mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testDefinedInAllBranches mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testNestedIf mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testRedefined mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testElif mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testVeryNestedIf mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testOmittedElse mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUpdatedInIf mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedInIf mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testTupleUnpack mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testFunction mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefFunc mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testVarDefinedInOuterScope mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testLambda mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testVarDefinedInOuterScopeUpdated mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testGenerator mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefClass mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testNonlocalVar mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testDefinedInOuterScopeNoError mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testScope mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testClassScope mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testGlobalDeclarationAfterUsage mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testFuncParams mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testForLoop mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testClassInsideFunction mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testDefinedDifferentBranchUsedBeforeDef mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testWhile mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testAssert mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testReturn mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testRaise mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testDefinedDifferentBranchPossiblyUndefined mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testBreak mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testContinue mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testNoReturn mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUnreachable mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testDictComprehension mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDef mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testWithStmt mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefImportBasicRename mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefImportsBasic mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefImportFromRename mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefImportFrom mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefFunctionDeclarations mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefBuiltins mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUsedBeforeDefImplicitModuleAttrs mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUntypedDef mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testUntypedDefCheckUntypedDefs
mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testTryMultiExcept mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testTryBasic mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testTryElse mypy/test/testcheck.py::TypeCheckSuite::check-possibly-undefined.test::testTryFinally