diff --git a/clang/lib/Format/TokenAnnotator.cpp b/clang/lib/Format/TokenAnnotator.cpp
index 70bcd7048c5..8cb786a4d34 100644
--- a/clang/lib/Format/TokenAnnotator.cpp
+++ b/clang/lib/Format/TokenAnnotator.cpp
@@ -2176,6 +2176,10 @@ static bool isFunctionDeclarationName(const FormatToken &Current,
         Next = Next->Next;
         continue;
       }
+      if (Next->is(TT_TemplateOpener) && Next->MatchingParen) {
+        Next = Next->MatchingParen;
+        continue;
+      }
 
       break;
     }
@@ -2705,20 +2709,40 @@ bool TokenAnnotator::spaceRequiredBetween(const AnnotatedLine &Line,
                                     tok::l_square));
   if (Right.is(tok::star) && Left.is(tok::l_paren))
     return false;
-  if (Right.isOneOf(tok::star, tok::amp, tok::ampamp) &&
-      (Left.is(tok::identifier) || Left.isSimpleTypeSpecifier()) &&
-      // Space between the type and the * in:
-      //   operator void*()
-      //   operator char*()
-      //   operator /*comment*/ const char*()
-      //   operator volatile /*comment*/ char*()
-      //   operator Foo*()
-      // dependent on PointerAlignment style.
-      Left.Previous &&
-      (Left.Previous->endsSequence(tok::kw_operator) ||
-       Left.Previous->endsSequence(tok::kw_const, tok::kw_operator) ||
-       Left.Previous->endsSequence(tok::kw_volatile, tok::kw_operator)))
-    return (Style.PointerAlignment != FormatStyle::PAS_Left);
+  if (Right.is(tok::star) && Left.is(tok::star))
+    return false;
+  if (Right.isOneOf(tok::star, tok::amp, tok::ampamp)) {
+    const FormatToken *Previous = &Left;
+    while (Previous && !Previous->is(tok::kw_operator)) {
+      if (Previous->is(tok::identifier) || Previous->isSimpleTypeSpecifier()) {
+        Previous = Previous->getPreviousNonComment();
+        continue;
+      }
+      if (Previous->is(TT_TemplateCloser) && Previous->MatchingParen) {
+        Previous = Previous->MatchingParen->getPreviousNonComment();
+        continue;
+      }
+      if (Previous->is(tok::coloncolon)) {
+        Previous = Previous->getPreviousNonComment();
+        continue;
+      }
+      break;
+    }
+    // Space between the type and the * in:
+    //   operator void*()
+    //   operator char*()
+    //   operator /*comment*/ const char*()
+    //   operator volatile /*comment*/ char*()
+    //   operator Foo*()
+    //   operator C<T>*()
+    //   operator std::Foo*()
+    //   operator C<T>::D<U>*()
+    // dependent on PointerAlignment style.
+    if (Previous && (Previous->endsSequence(tok::kw_operator) ||
+       Previous->endsSequence(tok::kw_const, tok::kw_operator) ||
+       Previous->endsSequence(tok::kw_volatile, tok::kw_operator)))
+      return (Style.PointerAlignment != FormatStyle::PAS_Left);
+  }
   const auto SpaceRequiredForArrayInitializerLSquare =
       [](const FormatToken &LSquareTok, const FormatStyle &Style) {
         return Style.SpacesInContainerLiterals ||
diff --git a/clang/unittests/Format/FormatTest.cpp b/clang/unittests/Format/FormatTest.cpp
index a5a26b5c1e8..7f8a3795e6e 100644
--- a/clang/unittests/Format/FormatTest.cpp
+++ b/clang/unittests/Format/FormatTest.cpp
@@ -6185,7 +6185,17 @@ TEST_F(FormatTest, ReturnTypeBreakingStyle) {
                "void\n"
                "A::operator[]() {}\n"
                "void\n"
-               "A::operator!() {}\n",
+               "A::operator!() {}\n"
+               "void\n"
+               "A::operator**() {}\n"
+               "void\n"
+               "A::operator<Foo> *() {}\n"
+               "void\n"
+               "A::operator<Foo> **() {}\n"
+               "void\n"
+               "A::operator<Foo> &() {}\n"
+               "void\n"
+               "A::operator void **() {}\n",
                Style);
   verifyFormat("constexpr auto\n"
                "operator()() const -> reference {}\n"
@@ -6202,6 +6212,10 @@ TEST_F(FormatTest, ReturnTypeBreakingStyle) {
                "constexpr auto\n"
                "operator void *() const -> reference {}\n"
                "constexpr auto\n"
+               "operator void **() const -> reference {}\n"
+               "constexpr auto\n"
+               "operator void *() const -> reference {}\n"
+               "constexpr auto\n"
                "operator void &() const -> reference {}\n"
                "constexpr auto\n"
                "operator void &&() const -> reference {}\n"
@@ -14986,9 +15000,20 @@ TEST_F(FormatTest, OperatorSpacing) {
   Style.PointerAlignment = FormatStyle::PAS_Right;
   verifyFormat("Foo::operator*();", Style);
   verifyFormat("Foo::operator void *();", Style);
+  verifyFormat("Foo::operator void **();", Style);
   verifyFormat("Foo::operator()(void *);", Style);
   verifyFormat("Foo::operator*(void *);", Style);
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator**();", Style);
+  verifyFormat("Foo::operator&();", Style);
+  verifyFormat("Foo::operator<int> *();", Style);
+  verifyFormat("Foo::operator<Foo> *();", Style);
+  verifyFormat("Foo::operator<int> **();", Style);
+  verifyFormat("Foo::operator<Foo> **();", Style);
+  verifyFormat("Foo::operator<int> &();", Style);
+  verifyFormat("Foo::operator<Foo> &();", Style);
+  verifyFormat("Foo::operator<int> &&();", Style);
+  verifyFormat("Foo::operator<Foo> &&();", Style);
   verifyFormat("operator*(int (*)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&();", Style);
@@ -14999,21 +15024,39 @@ TEST_F(FormatTest, OperatorSpacing) {
   verifyFormat("operator&(int (&)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&&();", Style);
+  verifyFormat("Foo::operator**();", Style);
   verifyFormat("Foo::operator void &&();", Style);
   verifyFormat("Foo::operator()(void &&);", Style);
   verifyFormat("Foo::operator&&(void &&);", Style);
   verifyFormat("Foo::operator&&();", Style);
   verifyFormat("operator&&(int(&&)(), class Foo);", Style);
+  verifyFormat("operator const nsTArrayRight<E> &()", Style);
+  verifyFormat("[[nodiscard]] operator const nsTArrayRight<E, Allocator> &()",
+               Style);
+  verifyFormat("operator void **()", Style);
+  verifyFormat("operator const FooRight<Object> &()", Style);
+  verifyFormat("operator const FooRight<Object> *()", Style);
+  verifyFormat("operator const FooRight<Object> **()", Style);
 
   Style.PointerAlignment = FormatStyle::PAS_Left;
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator**();", Style);
   verifyFormat("Foo::operator void*();", Style);
+  verifyFormat("Foo::operator void**();", Style);
   verifyFormat("Foo::operator/*comment*/ void*();", Style);
   verifyFormat("Foo::operator/*a*/ const /*b*/ void*();", Style);
   verifyFormat("Foo::operator/*a*/ volatile /*b*/ void*();", Style);
   verifyFormat("Foo::operator()(void*);", Style);
   verifyFormat("Foo::operator*(void*);", Style);
   verifyFormat("Foo::operator*();", Style);
+  verifyFormat("Foo::operator<int>*();", Style);
+  verifyFormat("Foo::operator<Foo>*();", Style);
+  verifyFormat("Foo::operator<int>**();", Style);
+  verifyFormat("Foo::operator<Foo>**();", Style);
+  verifyFormat("Foo::operator<int>&();", Style);
+  verifyFormat("Foo::operator<Foo>&();", Style);
+  verifyFormat("Foo::operator<int>&&();", Style);
+  verifyFormat("Foo::operator<Foo>&&();", Style);
   verifyFormat("operator*(int (*)(), class Foo);", Style);
 
   verifyFormat("Foo::operator&();", Style);
@@ -15035,6 +15078,21 @@ TEST_F(FormatTest, OperatorSpacing) {
   verifyFormat("Foo::operator&&(void&&);", Style);
   verifyFormat("Foo::operator&&();", Style);
   verifyFormat("operator&&(int(&&)(), class Foo);", Style);
+  verifyFormat("operator const nsTArrayLeft<E>&()", Style);
+  verifyFormat("[[nodiscard]] operator const nsTArrayLeft<E, Allocator>&()",
+               Style);
+  verifyFormat("operator void**()", Style);
+  verifyFormat("operator const FooLeft<Object>&()", Style);
+  verifyFormat("operator const FooLeft<Object>*()", Style);
+  verifyFormat("operator const FooLeft<Object>**()", Style);
+
+  // PR45107
+  verifyFormat("operator Vector<String>&();", Style);
+  verifyFormat("operator const Vector<String>&();", Style);
+  verifyFormat("operator foo::Bar*();", Style);
+  verifyFormat("operator const Foo<X>::Bar<Y>*();", Style);
+  verifyFormat("operator/*a*/ const /*b*/ Foo /*c*/<X> /*d*/ ::Bar<Y>*();",
+               Style);
 
   Style.PointerAlignment = FormatStyle::PAS_Middle;
   verifyFormat("Foo::operator*();", Style);