diff --git a/flang/docs/ParserCombinators.md b/flang/docs/ParserCombinators.md
index 7cb77deba2197..076e76f703c49 100644
--- a/flang/docs/ParserCombinators.md
+++ b/flang/docs/ParserCombinators.md
@@ -141,7 +141,7 @@ collect the values that they return.
 * `applyLambda([](&&x){}, p1, p2, ...)` is the same thing, but for lambdas
   and other function objects.
 * `applyMem(mf, p1, p2, ...)` is the same thing, but invokes a member
-  function of the result of the first parser for updates in place.
+  function of the result of the first parser.
 
 ### Token Parsers
 Last, we have these basic parsers on which the actual grammar of the Fortran
diff --git a/flang/include/flang/Parser/characters.h b/flang/include/flang/Parser/characters.h
index df188d674b9ee..dbdc058c44995 100644
--- a/flang/include/flang/Parser/characters.h
+++ b/flang/include/flang/Parser/characters.h
@@ -180,6 +180,8 @@ inline constexpr bool IsValidFortranTokenCharacter(char ch) {
   case '>':
   case '[':
   case ']':
+  case '{': // Used in OpenMP context selector specification
+  case '}': //
     return true;
   default:
     return IsLegalIdentifierStart(ch) || IsDecimalDigit(ch);
diff --git a/flang/include/flang/Parser/dump-parse-tree.h b/flang/include/flang/Parser/dump-parse-tree.h
index 3331520922bc6..11725991e9c9a 100644
--- a/flang/include/flang/Parser/dump-parse-tree.h
+++ b/flang/include/flang/Parser/dump-parse-tree.h
@@ -476,6 +476,19 @@ class ParseTreeDumper {
   NODE(parser, NullInit)
   NODE(parser, ObjectDecl)
   NODE(parser, OldParameterStmt)
+  NODE(parser, OmpTraitPropertyName)
+  NODE(parser, OmpTraitScore)
+  NODE(parser, OmpTraitPropertyExtension)
+  NODE(OmpTraitPropertyExtension, ExtensionValue)
+  NODE(parser, OmpTraitProperty)
+  NODE(parser, OmpTraitSelectorName)
+  NODE_ENUM(OmpTraitSelectorName, Value)
+  NODE(parser, OmpTraitSelector)
+  NODE(OmpTraitSelector, Properties)
+  NODE(parser, OmpTraitSetSelectorName)
+  NODE_ENUM(OmpTraitSetSelectorName, Value)
+  NODE(parser, OmpTraitSetSelector)
+  NODE(parser, OmpContextSelectorSpecification)
   NODE(parser, OmpMapper)
   NODE(parser, OmpMapType)
   NODE_ENUM(OmpMapType, Value)
diff --git a/flang/include/flang/Parser/parse-tree.h b/flang/include/flang/Parser/parse-tree.h
index 941d70d387629..00d85aa05fb3a 100644
--- a/flang/include/flang/Parser/parse-tree.h
+++ b/flang/include/flang/Parser/parse-tree.h
@@ -3453,6 +3453,9 @@ WRAPPER_CLASS(PauseStmt, std::optional<StopCode>);
 
 // --- Common definitions
 
+struct OmpClause;
+struct OmpClauseList;
+
 // 2.1 Directives or clauses may accept a list or extended-list.
 //     A list item is a variable, array section or common block name (enclosed
 //     in slashes). An extended list item is a list item or a procedure Name.
@@ -3474,6 +3477,150 @@ WRAPPER_CLASS(OmpObjectList, std::list<OmpObject>);
 
 #define MODIFIERS() std::optional<std::list<Modifier>>
 
+inline namespace traits {
+// trait-property-name ->
+//    identifier | string-literal
+//
+// This is a bit of a problematic case. The spec says that a word in quotes,
+// and the same word without quotes are equivalent. We currently parse both
+// as a string, but it's likely just a temporary solution.
+//
+// The problem is that trait-property can be (among other things) a
+// trait-property-name or a trait-property-expression. A simple identifier
+// can be either, there is no reasonably simple way of telling them apart
+// in the parser. There is a similar issue with extensions. Some of that
+// disambiguation may need to be done in the "canonicalization" pass and
+// then some of those AST nodes would be rewritten into different ones.
+//
+struct OmpTraitPropertyName {
+  CharBlock source;
+  WRAPPER_CLASS_BOILERPLATE(OmpTraitPropertyName, std::string);
+};
+
+// trait-score ->
+//    SCORE(non-negative-const-integer-expression)
+struct OmpTraitScore {
+  CharBlock source;
+  WRAPPER_CLASS_BOILERPLATE(OmpTraitScore, ScalarIntExpr);
+};
+
+// trait-property-extension ->
+//    trait-property-name (trait-property-value, ...)
+// trait-property-value ->
+//    trait-property-name |
+//    scalar-integer-expression |
+//    trait-property-extension
+//
+// The grammar in OpenMP 5.2+ spec is ambiguous, the above is a different
+// version (but equivalent) that doesn't have ambiguities.
+// The ambiguity is in
+//   trait-property:
+//      trait-property-name          <- (a)
+//      trait-property-clause
+//      trait-property-expression    <- (b)
+//      trait-property-extension     <- this conflicts with (a) and (b)
+//   trait-property-extension:
+//      trait-property-name          <- conflict with (a)
+//      identifier(trait-property-extension[, trait-property-extension[, ...]])
+//      constant integer expression  <- conflict with (b)
+//
+struct OmpTraitPropertyExtension {
+  CharBlock source;
+  TUPLE_CLASS_BOILERPLATE(OmpTraitPropertyExtension);
+  struct ExtensionValue {
+    CharBlock source;
+    UNION_CLASS_BOILERPLATE(ExtensionValue);
+    std::variant<OmpTraitPropertyName, ScalarExpr,
+        common::Indirection<OmpTraitPropertyExtension>>
+        u;
+  };
+  using ExtensionList = std::list<ExtensionValue>;
+  std::tuple<OmpTraitPropertyName, ExtensionList> t;
+};
+
+// trait-property ->
+//    trait-property-name | OmpClause |
+//    trait-property-expression | trait-property-extension
+// trait-property-expression ->
+//    scalar-logical-expression | scalar-integer-expression
+//
+// The parser for a logical expression will accept an integer expression,
+// and if it's not logical, it will flag an error later. The same thing
+// will happen if the scalar integer expression sees a logical expresion.
+// To avoid this, parse all expressions as scalar expressions.
+struct OmpTraitProperty {
+  CharBlock source;
+  UNION_CLASS_BOILERPLATE(OmpTraitProperty);
+  std::variant<OmpTraitPropertyName, common::Indirection<OmpClause>,
+      ScalarExpr, // trait-property-expresion
+      OmpTraitPropertyExtension>
+      u;
+};
+
+// trait-selector-name ->
+//    KIND |              DT       // name-list (host, nohost, +/add-def-doc)
+//    ISA |               DT       // name-list (isa_name, ... /impl-defined)
+//    ARCH |              DT       // name-list (arch_name, ... /impl-defined)
+//    directive-name |    C        // no properties
+//    SIMD |              C        // clause-list (from declare_simd)
+//                                 // (at least simdlen, inbranch/notinbranch)
+//    DEVICE_NUM |        T        // device-number
+//    UID |               T        // unique-string-id /impl-defined
+//    VENDOR |            I        // name-list (vendor-id /add-def-doc)
+//    EXTENSION |         I        // name-list (ext_name /impl-defined)
+//    ATOMIC_DEFAULT_MEM_ORDER I | // value of admo
+//    REQUIRES |          I        // clause-list (from requires)
+//    CONDITION           U        // logical-expr
+//
+// Trait-set-selectors:
+//    [D]evice, [T]arget_device, [C]onstruct, [I]mplementation, [U]ser.
+struct OmpTraitSelectorName {
+  CharBlock source;
+  UNION_CLASS_BOILERPLATE(OmpTraitSelectorName);
+  ENUM_CLASS(Value, Arch, Atomic_Default_Mem_Order, Condition, Device_Num,
+      Extension, Isa, Kind, Requires, Simd, Uid, Vendor)
+  std::variant<Value, llvm::omp::Directive> u;
+};
+
+// trait-selector ->
+//    trait-selector-name |
+//    trait-selector-name ([trait-score:] trait-property, ...)
+struct OmpTraitSelector {
+  CharBlock source;
+  TUPLE_CLASS_BOILERPLATE(OmpTraitSelector);
+  struct Properties {
+    TUPLE_CLASS_BOILERPLATE(Properties);
+    std::tuple<std::optional<OmpTraitScore>, std::list<OmpTraitProperty>> t;
+  };
+  std::tuple<OmpTraitSelectorName, std::optional<Properties>> t;
+};
+
+// trait-set-selector-name ->
+//    CONSTRUCT | DEVICE | IMPLEMENTATION | USER |  // since 5.0
+//    TARGET_DEVICE                                 // since 5.1
+struct OmpTraitSetSelectorName {
+  CharBlock source;
+  ENUM_CLASS(Value, Construct, Device, Implementation, Target_Device, User)
+  WRAPPER_CLASS_BOILERPLATE(OmpTraitSetSelectorName, Value);
+};
+
+// trait-set-selector ->
+//    trait-set-selector-name = {trait-selector, ...}
+struct OmpTraitSetSelector {
+  CharBlock source;
+  TUPLE_CLASS_BOILERPLATE(OmpTraitSetSelector);
+  std::tuple<OmpTraitSetSelectorName, std::list<OmpTraitSelector>> t;
+};
+
+// context-selector-specification ->
+//    trait-set-selector, ...
+struct OmpContextSelectorSpecification { // Modifier
+  CharBlock source;
+  WRAPPER_CLASS_BOILERPLATE(
+      OmpContextSelectorSpecification, std::list<OmpTraitSetSelector>);
+};
+} // namespace traits
+
 inline namespace modifier {
 // For uniformity, in all keyword modifiers the name of the type defined
 // by ENUM_CLASS is "Value", e.g.
@@ -3744,6 +3891,9 @@ struct OmpVariableCategory {
   ENUM_CLASS(Value, Aggregate, All, Allocatable, Pointer, Scalar)
   WRAPPER_CLASS_BOILERPLATE(OmpVariableCategory, Value);
 };
+
+// context-selector
+using OmpContextSelector = traits::OmpContextSelectorSpecification;
 } // namespace modifier
 
 // --- Clauses
diff --git a/flang/lib/Parser/basic-parsers.h b/flang/lib/Parser/basic-parsers.h
index 515b5993d6737..1a8c14e7048f6 100644
--- a/flang/lib/Parser/basic-parsers.h
+++ b/flang/lib/Parser/basic-parsers.h
@@ -580,11 +580,11 @@ template <typename PA> inline constexpr auto defaulted(PA p) {
 // applyLambda(f, ...) is the same concept extended to std::function<> functors.
 // It is not constexpr.
 //
-// Member function application is supported by applyMem(f, a).  If the
-// parser a succeeds and returns some value ax, the result is that returned
-// by ax.f().  Additional parser arguments can be specified to supply their
-// results to the member function call, so applyMem(f, a, b) succeeds if
-// both a and b do so and returns the result of calling ax.f(std::move(bx)).
+// Member function application is supported by applyMem(&C::f, a).  If the
+// parser a succeeds and returns some value ax of type C, the result is that
+// returned by ax.f().  Additional parser arguments can be specified to supply
+// their results to the member function call, so applyMem(&C::f, a, b) succeeds
+// if both a and b do so and returns the result of calling ax.f(std::move(bx)).
 
 // Runs a sequence of parsers until one fails or all have succeeded.
 // Collects their results in a std::tuple<std::optional<>...>.
@@ -654,39 +654,31 @@ inline /* not constexpr */ auto applyLambda(
 }
 
 // Member function application
-template <typename OBJPARSER, typename... PARSER> class AMFPHelper {
-  using resultType = typename OBJPARSER::resultType;
-
-public:
-  using type = void (resultType::*)(typename PARSER::resultType &&...);
-};
-template <typename OBJPARSER, typename... PARSER>
-using ApplicableMemberFunctionPointer =
-    typename AMFPHelper<OBJPARSER, PARSER...>::type;
-
-template <typename OBJPARSER, typename... PARSER, std::size_t... J>
-inline auto ApplyHelperMember(
-    ApplicableMemberFunctionPointer<OBJPARSER, PARSER...> mfp,
-    ApplyArgs<OBJPARSER, PARSER...> &&args, std::index_sequence<J...>) ->
-    typename OBJPARSER::resultType {
-  ((*std::get<0>(args)).*mfp)(std::move(*std::get<J + 1>(args))...);
-  return std::get<0>(std::move(args));
+template <typename MEMFUNC, typename OBJPARSER, typename... PARSER,
+    std::size_t... J>
+inline auto ApplyHelperMember(MEMFUNC mfp,
+    ApplyArgs<OBJPARSER, PARSER...> &&args, std::index_sequence<J...>) {
+  return ((*std::get<0>(args)).*mfp)(std::move(*std::get<J + 1>(args))...);
 }
 
-template <typename OBJPARSER, typename... PARSER> class ApplyMemberFunction {
-  using funcType = ApplicableMemberFunctionPointer<OBJPARSER, PARSER...>;
+template <typename MEMFUNC, typename OBJPARSER, typename... PARSER>
+class ApplyMemberFunction {
+  static_assert(std::is_member_function_pointer_v<MEMFUNC>);
+  using funcType = MEMFUNC;
 
 public:
-  using resultType = typename OBJPARSER::resultType;
+  using resultType =
+      std::invoke_result_t<MEMFUNC, typename OBJPARSER::resultType, PARSER...>;
+
   constexpr ApplyMemberFunction(const ApplyMemberFunction &) = default;
-  constexpr ApplyMemberFunction(funcType f, OBJPARSER o, PARSER... p)
+  constexpr ApplyMemberFunction(MEMFUNC f, OBJPARSER o, PARSER... p)
       : function_{f}, parsers_{o, p...} {}
   std::optional<resultType> Parse(ParseState &state) const {
     ApplyArgs<OBJPARSER, PARSER...> results;
     using Sequence1 = std::index_sequence_for<OBJPARSER, PARSER...>;
     using Sequence2 = std::index_sequence_for<PARSER...>;
     if (ApplyHelperArgs(parsers_, results, state, Sequence1{})) {
-      return ApplyHelperMember<OBJPARSER, PARSER...>(
+      return ApplyHelperMember<MEMFUNC, OBJPARSER, PARSER...>(
           function_, std::move(results), Sequence2{});
     } else {
       return std::nullopt;
@@ -698,11 +690,11 @@ template <typename OBJPARSER, typename... PARSER> class ApplyMemberFunction {
   const std::tuple<OBJPARSER, PARSER...> parsers_;
 };
 
-template <typename OBJPARSER, typename... PARSER>
+template <typename MEMFUNC, typename OBJPARSER, typename... PARSER>
 inline constexpr auto applyMem(
-    ApplicableMemberFunctionPointer<OBJPARSER, PARSER...> mfp,
-    const OBJPARSER &objParser, PARSER... parser) {
-  return ApplyMemberFunction<OBJPARSER, PARSER...>{mfp, objParser, parser...};
+    MEMFUNC memfn, const OBJPARSER &objParser, PARSER... parser) {
+  return ApplyMemberFunction<MEMFUNC, OBJPARSER, PARSER...>{
+      memfn, objParser, parser...};
 }
 
 // As is done with function application via applyFunction() above, class
diff --git a/flang/lib/Parser/openmp-parsers.cpp b/flang/lib/Parser/openmp-parsers.cpp
index 894c458a335b2..5ff91da082c85 100644
--- a/flang/lib/Parser/openmp-parsers.cpp
+++ b/flang/lib/Parser/openmp-parsers.cpp
@@ -153,6 +153,83 @@ static TypeDeclarationStmt makeIterSpecDecl(std::list<ObjectName> &&names) {
       makeEntityList(std::move(names)));
 }
 
+// --- Parsers for context traits -------------------------------------
+
+static std::string nameToString(Name &&name) { return name.ToString(); }
+
+TYPE_PARSER(sourced(construct<OmpTraitPropertyName>( //
+    (space >> charLiteralConstantWithoutKind) ||
+    applyFunction(nameToString, Parser<Name>{}))))
+
+TYPE_PARSER(sourced(construct<OmpTraitScore>( //
+    "SCORE" >> parenthesized(scalarIntExpr))))
+
+TYPE_PARSER(sourced(construct<OmpTraitPropertyExtension::ExtensionValue>(
+    // Parse nested extension first.
+    construct<OmpTraitPropertyExtension::ExtensionValue>(
+        indirect(Parser<OmpTraitPropertyExtension>{})) ||
+    construct<OmpTraitPropertyExtension::ExtensionValue>(
+        Parser<OmpTraitPropertyName>{}) ||
+    construct<OmpTraitPropertyExtension::ExtensionValue>(scalarExpr))))
+
+TYPE_PARSER(sourced(construct<OmpTraitPropertyExtension>( //
+    Parser<OmpTraitPropertyName>{},
+    parenthesized(nonemptySeparated(
+        Parser<OmpTraitPropertyExtension::ExtensionValue>{}, ","_tok)))))
+
+TYPE_PARSER(sourced(construct<OmpTraitProperty>(
+    // Try clause first, then extension before OmpTraitPropertyName.
+    construct<OmpTraitProperty>(indirect(Parser<OmpClause>{})) ||
+    construct<OmpTraitProperty>(Parser<OmpTraitPropertyExtension>{}) ||
+    construct<OmpTraitProperty>(Parser<OmpTraitPropertyName>{}) ||
+    construct<OmpTraitProperty>(scalarExpr))))
+
+TYPE_PARSER(construct<OmpTraitSelectorName::Value>(
+    "ARCH" >> pure(OmpTraitSelectorName::Value::Arch) ||
+    "ATOMIC_DEFAULT_MEM_ORDER" >>
+        pure(OmpTraitSelectorName::Value::Atomic_Default_Mem_Order) ||
+    "CONDITION" >> pure(OmpTraitSelectorName::Value::Condition) ||
+    "DEVICE_NUM" >> pure(OmpTraitSelectorName::Value::Device_Num) ||
+    "EXTENSION" >> pure(OmpTraitSelectorName::Value::Extension) ||
+    "ISA" >> pure(OmpTraitSelectorName::Value::Isa) ||
+    "KIND" >> pure(OmpTraitSelectorName::Value::Kind) ||
+    "REQUIRES" >> pure(OmpTraitSelectorName::Value::Requires) ||
+    "SIMD" >> pure(OmpTraitSelectorName::Value::Simd) ||
+    "UID" >> pure(OmpTraitSelectorName::Value::Uid) ||
+    "VENDOR" >> pure(OmpTraitSelectorName::Value::Vendor)))
+
+TYPE_PARSER(sourced(construct<OmpTraitSelectorName>(
+    // Parse predefined names first (because of SIMD).
+    construct<OmpTraitSelectorName>(Parser<OmpTraitSelectorName::Value>{}) ||
+    construct<OmpTraitSelectorName>(OmpDirectiveNameParser{}))))
+
+TYPE_PARSER(construct<OmpTraitSelector::Properties>(
+    maybe(Parser<OmpTraitScore>{} / ":"_tok),
+    nonemptySeparated(Parser<OmpTraitProperty>{}, ","_tok)))
+
+TYPE_PARSER(sourced(construct<OmpTraitSelector>( //
+    Parser<OmpTraitSelectorName>{}, //
+    maybe(parenthesized(Parser<OmpTraitSelector::Properties>{})))))
+
+TYPE_PARSER(construct<OmpTraitSetSelectorName::Value>(
+    "CONSTRUCT" >> pure(OmpTraitSetSelectorName::Value::Construct) ||
+    "DEVICE" >> pure(OmpTraitSetSelectorName::Value::Device) ||
+    "IMPLEMENTATION" >> pure(OmpTraitSetSelectorName::Value::Implementation) ||
+    "TARGET_DEVICE" >> pure(OmpTraitSetSelectorName::Value::Target_Device) ||
+    "USER" >> pure(OmpTraitSetSelectorName::Value::User)))
+
+TYPE_PARSER(sourced(construct<OmpTraitSetSelectorName>(
+    Parser<OmpTraitSetSelectorName::Value>{})))
+
+TYPE_PARSER(sourced(construct<OmpTraitSetSelector>( //
+    Parser<OmpTraitSetSelectorName>{},
+    "=" >> braced(nonemptySeparated(Parser<OmpTraitSelector>{}, ","_tok)))))
+
+TYPE_PARSER(sourced(construct<OmpContextSelectorSpecification>(
+    nonemptySeparated(Parser<OmpTraitSetSelector>{}, ","_tok))))
+
+// Parser<OmpContextSelector> == Parser<traits::OmpContextSelectorSpecification>
+
 // --- Parsers for clause modifiers -----------------------------------
 
 TYPE_PARSER(construct<OmpAlignment>(scalarIntExpr))
diff --git a/flang/lib/Parser/token-parsers.h b/flang/lib/Parser/token-parsers.h
index fe6bc1f69f576..3e0c59b89d964 100644
--- a/flang/lib/Parser/token-parsers.h
+++ b/flang/lib/Parser/token-parsers.h
@@ -215,6 +215,10 @@ template <class PA> inline constexpr auto bracketed(const PA &p) {
   return "[" >> p / "]";
 }
 
+template <class PA> inline constexpr auto braced(const PA &p) {
+  return "{" >> p / "}";
+}
+
 // Quoted character literal constants.
 struct CharLiteralChar {
   using resultType = std::pair<char, bool /* was escaped */>;
diff --git a/flang/lib/Parser/unparse.cpp b/flang/lib/Parser/unparse.cpp
index 58820476c51bc..7bf404bba2c3e 100644
--- a/flang/lib/Parser/unparse.cpp
+++ b/flang/lib/Parser/unparse.cpp
@@ -2067,6 +2067,38 @@ class UnparseVisitor {
   }
 
   // OpenMP Clauses & Directives
+  void Unparse(const llvm::omp::Directive &x) {
+    Word(llvm::omp::getOpenMPDirectiveName(x).str());
+  }
+  void Unparse(const OmpTraitScore &x) {
+    Word("SCORE(");
+    Walk(x.v);
+    Put(")");
+  }
+  void Unparse(const OmpTraitPropertyExtension &x) {
+    Walk(std::get<OmpTraitPropertyName>(x.t));
+    Put("(");
+    Walk(std::get<OmpTraitPropertyExtension::ExtensionList>(x.t), ",");
+    Put(")");
+  }
+  void Unparse(const OmpTraitSelector &x) {
+    Walk(std::get<OmpTraitSelectorName>(x.t));
+    Walk(std::get<std::optional<OmpTraitSelector::Properties>>(x.t));
+  }
+  void Unparse(const OmpTraitSelector::Properties &x) {
+    Put("(");
+    Walk(std::get<std::optional<OmpTraitScore>>(x.t), ": ");
+    Walk(std::get<std::list<OmpTraitProperty>>(x.t));
+    Put(")");
+  }
+  void Unparse(const OmpTraitSetSelector &x) {
+    Walk(std::get<OmpTraitSetSelectorName>(x.t));
+    Put("={");
+    Walk(std::get<std::list<OmpTraitSelector>>(x.t));
+    Put("}");
+  }
+  void Unparse(const OmpContextSelectorSpecification &x) { Walk(x.v, ", "); }
+
   void Unparse(const OmpObject &x) {
     common::visit(common::visitors{
                       [&](const Designator &y) { Walk(y); },
@@ -2916,6 +2948,9 @@ class UnparseVisitor {
   WALK_NESTED_ENUM(OmpPrescriptiveness, Value) // OMP prescriptiveness
   WALK_NESTED_ENUM(OmpMapType, Value) // OMP map-type
   WALK_NESTED_ENUM(OmpMapTypeModifier, Value) // OMP map-type-modifier
+  WALK_NESTED_ENUM(OmpTraitSelectorName, Value)
+  WALK_NESTED_ENUM(OmpTraitSetSelectorName, Value)
+
 #undef WALK_NESTED_ENUM
   void Unparse(const ReductionOperator::Operator x) {
     switch (x) {