Index: clangd/CodeComplete.cpp
===================================================================
--- clangd/CodeComplete.cpp
+++ clangd/CodeComplete.cpp
@@ -1510,6 +1510,13 @@
   }
 };
 
+template <class T> bool isExplicitTemplateSpecialization(const NamedDecl &ND) {
+  if (const auto *TD = dyn_cast<T>(&ND))
+    if (TD->getTemplateSpecializationKind() == TSK_ExplicitSpecialization)
+      return true;
+  return false;
+}
+
 } // namespace
 
 clang::CodeCompleteOptions CodeCompleteOptions::getClangCompleteOpts() const {
@@ -1603,6 +1610,13 @@
     };
     return false;
   };
+  // We only complete symbol's name, which is the same as the name of the
+  // *primary* template in case of template specializations.
+  if (isExplicitTemplateSpecialization<FunctionDecl>(ND) ||
+      isExplicitTemplateSpecialization<CXXRecordDecl>(ND) ||
+      isExplicitTemplateSpecialization<VarDecl>(ND))
+    return false;
+
   if (InTopLevelScope(ND))
     return true;
 
Index: clangd/index/MemIndex.cpp
===================================================================
--- clangd/index/MemIndex.cpp
+++ clangd/index/MemIndex.cpp
@@ -11,6 +11,7 @@
 #include "Logger.h"
 #include "Quality.h"
 #include "Trace.h"
+#include "clang/Index/IndexSymbol.h"
 
 namespace clang {
 namespace clangd {
@@ -37,6 +38,15 @@
   for (const auto Pair : Index) {
     const Symbol *Sym = Pair.second;
 
+    // FIXME: Enable fuzzy find on template specializations once we start
+    // storing template arguments in the name. Currently we only store name for
+    // class template, which would cause duplication in the results.
+    if (Sym->SymInfo.Properties &
+        (static_cast<index::SymbolPropertySet>(
+             index::SymbolProperty::TemplateSpecialization) |
+         static_cast<index::SymbolPropertySet>(
+             index::SymbolProperty::TemplatePartialSpecialization)))
+      continue;
     // Exact match against all possible scopes.
     if (!Req.AnyScope && !llvm::is_contained(Req.Scopes, Sym->Scope))
       continue;
Index: clangd/index/SymbolCollector.cpp
===================================================================
--- clangd/index/SymbolCollector.cpp
+++ clangd/index/SymbolCollector.cpp
@@ -221,13 +221,6 @@
   return static_cast<RefKind>(static_cast<unsigned>(RefKind::All) & Roles);
 }
 
-template <class T> bool explicitTemplateSpecialization(const NamedDecl &ND) {
-  if (const auto *TD = dyn_cast<T>(&ND))
-    if (TD->getTemplateSpecializationKind() == TSK_ExplicitSpecialization)
-      return true;
-  return false;
-}
-
 } // namespace
 
 SymbolCollector::SymbolCollector(Options Opts) : Opts(std::move(Opts)) {}
@@ -279,10 +272,6 @@
     if (!isa<RecordDecl>(DeclCtx))
       return false;
   }
-  if (explicitTemplateSpecialization<FunctionDecl>(ND) ||
-      explicitTemplateSpecialization<CXXRecordDecl>(ND) ||
-      explicitTemplateSpecialization<VarDecl>(ND))
-    return false;
 
   // Avoid indexing internal symbols in protobuf generated headers.
   if (isPrivateProtoDecl(ND))
Index: clangd/index/dex/Dex.cpp
===================================================================
--- clangd/index/dex/Dex.cpp
+++ clangd/index/dex/Dex.cpp
@@ -86,6 +86,15 @@
   llvm::DenseMap<Token, std::vector<DocID>> TempInvertedIndex;
   for (DocID SymbolRank = 0; SymbolRank < Symbols.size(); ++SymbolRank) {
     const auto *Sym = Symbols[SymbolRank];
+    // FIXME: Enable fuzzy find on template specializations once we start
+    // storing template arguments in the name. Currently we only store name for
+    // class template, which would cause duplication in the results.
+    if (Sym->SymInfo.Properties &
+        (static_cast<index::SymbolPropertySet>(
+             index::SymbolProperty::TemplateSpecialization) |
+         static_cast<index::SymbolPropertySet>(
+             index::SymbolProperty::TemplatePartialSpecialization)))
+      continue;
     for (const auto &Token : generateSearchTokens(*Sym))
       TempInvertedIndex[Token].push_back(SymbolRank);
   }
Index: unittests/clangd/DexTests.cpp
===================================================================
--- unittests/clangd/DexTests.cpp
+++ unittests/clangd/DexTests.cpp
@@ -710,6 +710,41 @@
   EXPECT_THAT(match(I, Req), ElementsAre("t2"));
 }
 
+TEST(DexTest, TemplateSpecialization) {
+  SymbolSlab::Builder B;
+
+  Symbol S = symbol("TempSpec");
+  S.ID = SymbolID("0");
+  B.insert(S);
+
+  S = symbol("TempSpec");
+  S.ID = SymbolID("1");
+  S.SymInfo.Properties = static_cast<index::SymbolPropertySet>(
+      index::SymbolProperty::TemplateSpecialization);
+  B.insert(S);
+
+  S = symbol("TempSpec");
+  S.ID = SymbolID("2");
+  S.SymInfo.Properties = static_cast<index::SymbolPropertySet>(
+      index::SymbolProperty::TemplatePartialSpecialization);
+  B.insert(S);
+
+  auto I = dex::Dex::build(std::move(B).build(), RefSlab());
+  FuzzyFindRequest Req;
+  Req.Query = "TempSpec";
+  Req.AnyScope = true;
+
+  std::vector<Symbol> Symbols;
+  I->fuzzyFind(Req, [&Symbols](const Symbol &Sym) { Symbols.push_back(Sym); });
+  EXPECT_EQ(Symbols.size(), 1U);
+  EXPECT_FALSE(Symbols.front().SymInfo.Properties &
+               static_cast<index::SymbolPropertySet>(
+                   index::SymbolProperty::TemplateSpecialization));
+  EXPECT_FALSE(Symbols.front().SymInfo.Properties &
+               static_cast<index::SymbolPropertySet>(
+                   index::SymbolProperty::TemplatePartialSpecialization));
+}
+
 } // namespace
 } // namespace dex
 } // namespace clangd
Index: unittests/clangd/IndexTests.cpp
===================================================================
--- unittests/clangd/IndexTests.cpp
+++ unittests/clangd/IndexTests.cpp
@@ -13,6 +13,8 @@
 #include "index/Index.h"
 #include "index/MemIndex.h"
 #include "index/Merge.h"
+#include "index/Symbol.h"
+#include "clang/Index/IndexSymbol.h"
 #include "gmock/gmock.h"
 #include "gtest/gtest.h"
 
@@ -181,6 +183,41 @@
   EXPECT_THAT(lookup(*I, SymbolID("ns::nonono")), UnorderedElementsAre());
 }
 
+TEST(MemIndexTest, TemplateSpecialization) {
+  SymbolSlab::Builder B;
+
+  Symbol S = symbol("TempSpec");
+  S.ID = SymbolID("0");
+  B.insert(S);
+
+  S = symbol("TempSpec");
+  S.ID = SymbolID("1");
+  S.SymInfo.Properties = static_cast<index::SymbolPropertySet>(
+      index::SymbolProperty::TemplateSpecialization);
+  B.insert(S);
+
+  S = symbol("TempSpec");
+  S.ID = SymbolID("2");
+  S.SymInfo.Properties = static_cast<index::SymbolPropertySet>(
+      index::SymbolProperty::TemplatePartialSpecialization);
+  B.insert(S);
+
+  auto I = MemIndex::build(std::move(B).build(), RefSlab());
+  FuzzyFindRequest Req;
+  Req.Query = "TempSpec";
+  Req.AnyScope = true;
+
+  std::vector<Symbol> Symbols;
+  I->fuzzyFind(Req, [&Symbols](const Symbol &Sym) { Symbols.push_back(Sym); });
+  EXPECT_EQ(Symbols.size(), 1U);
+  EXPECT_FALSE(Symbols.front().SymInfo.Properties &
+               static_cast<index::SymbolPropertySet>(
+                   index::SymbolProperty::TemplateSpecialization));
+  EXPECT_FALSE(Symbols.front().SymInfo.Properties &
+               static_cast<index::SymbolPropertySet>(
+                   index::SymbolProperty::TemplatePartialSpecialization));
+}
+
 TEST(MergeIndexTest, Lookup) {
   auto I = MemIndex::build(generateSymbols({"ns::A", "ns::B"}), RefSlab()),
        J = MemIndex::build(generateSymbols({"ns::B", "ns::C"}), RefSlab());
Index: unittests/clangd/SymbolCollectorTests.cpp
===================================================================
--- unittests/clangd/SymbolCollectorTests.cpp
+++ unittests/clangd/SymbolCollectorTests.cpp
@@ -392,17 +392,25 @@
 
 TEST_F(SymbolCollectorTest, Template) {
   Annotations Header(R"(
-    // Template is indexed, specialization and instantiation is not.
-    template <class T> struct [[Tmpl]] {T $xdecl[[x]] = 0;};
-    template <> struct Tmpl<int> {};
-    extern template struct Tmpl<float>;
-    template struct Tmpl<double>;
+    // Primary template and explicit specialization are indexed, instantiation
+    // is not.
+    template <class T, class U> struct [[Tmpl]] {T $xdecl[[x]] = 0;};
+    template <> struct $specdecl[[Tmpl]]<int, bool> {};
+    template <class U> struct $partspecdecl[[Tmpl]]<bool, U> {};
+    extern template struct Tmpl<float, bool>;
+    template struct Tmpl<double, bool>;
   )");
   runSymbolCollector(Header.code(), /*Main=*/"");
   EXPECT_THAT(Symbols,
-              UnorderedElementsAreArray(
-                  {AllOf(QName("Tmpl"), DeclRange(Header.range())),
-                   AllOf(QName("Tmpl::x"), DeclRange(Header.range("xdecl")))}));
+              UnorderedElementsAre(
+                  AllOf(QName("Tmpl"), DeclRange(Header.range()),
+                        ForCodeCompletion(true)),
+                  AllOf(QName("Tmpl"), DeclRange(Header.range("specdecl")),
+                        ForCodeCompletion(false)),
+                  AllOf(QName("Tmpl"), DeclRange(Header.range("partspecdecl")),
+                        ForCodeCompletion(false)),
+                  AllOf(QName("Tmpl::x"), DeclRange(Header.range("xdecl")),
+                        ForCodeCompletion(false))));
 }
 
 TEST_F(SymbolCollectorTest, ObjCSymbols) {