diff --git a/CHANGELOG.md b/CHANGELOG.md
index 03597647efe9e..2dd294a966f9e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -25,6 +25,10 @@ CHANGELOG
 Swift 5.1
 ---------
 
+* [SE-0068][]:
+
+  `Self` can now be used inside member functions and for function arguments of structs and enums to refer to the containing type.
+
 * [SR-7799][]:
 
   Enum cases can now be matched against an optional enum without
diff --git a/lib/AST/DeclContext.cpp b/lib/AST/DeclContext.cpp
index 1951dd0e73dd6..33af8d76293dd 100644
--- a/lib/AST/DeclContext.cpp
+++ b/lib/AST/DeclContext.cpp
@@ -223,9 +223,8 @@ bool DeclContext::isTypeContext() const {
 DeclContext *DeclContext::getInnermostTypeContext() {
   auto dc = this;
   do {
-    if (auto decl = dc->getAsDecl())
-      if (isa<NominalTypeDecl>(decl) || isa<ExtensionDecl>(decl))
-        return dc;
+    if (dc->isTypeContext())
+      return dc;
   } while ((dc = dc->getParent()));
 
   return nullptr;
diff --git a/lib/Sema/TypeCheckConstraints.cpp b/lib/Sema/TypeCheckConstraints.cpp
index 5574e65ada1f8..daee66f83b21d 100644
--- a/lib/Sema/TypeCheckConstraints.cpp
+++ b/lib/Sema/TypeCheckConstraints.cpp
@@ -551,6 +551,18 @@ resolveDeclRefExpr(UnresolvedDeclRefExpr *UDRE, DeclContext *DC) {
     };
 
     if (!isConfused) {
+      if (Name == Context.Id_Self) {
+        if (DeclContext *typeContext = DC->getInnermostTypeContext()){
+          Type SelfType = typeContext->getSelfInterfaceType();
+
+          if (typeContext->getSelfClassDecl())
+            SelfType = DynamicSelfType::get(SelfType, Context);
+          SelfType = DC->mapTypeIntoContext(SelfType);
+          return new (Context) TypeExpr(TypeLoc(new (Context)
+                                                FixedTypeRepr(SelfType, Loc)));
+        }
+      }
+
       TypoCorrectionResults corrections(*this, Name, nameLoc);
       performTypoCorrection(DC, UDRE->getRefKind(), Type(),
                             lookupOptions, corrections);
diff --git a/lib/Sema/TypeCheckType.cpp b/lib/Sema/TypeCheckType.cpp
index 9cece60fca78a..07a79cebe8b6e 100644
--- a/lib/Sema/TypeCheckType.cpp
+++ b/lib/Sema/TypeCheckType.cpp
@@ -1057,10 +1057,23 @@ static Type diagnoseUnknownType(TypeResolution resolution,
       NominalTypeDecl *nominal = nullptr;
       if ((nominalDC = dc->getInnermostTypeContext()) &&
           (nominal = nominalDC->getSelfNominalTypeDecl())) {
-        // Attempt to refer to 'Self' within a non-protocol nominal
-        // type. Fix this by replacing 'Self' with the nominal type name.
         assert(!isa<ProtocolDecl>(nominal) && "Cannot be a protocol");
 
+        bool insideClass = nominalDC->getSelfClassDecl() != nullptr;
+        AbstractFunctionDecl *methodDecl = dc->getInnermostMethodContext();
+        bool declaringMethod = methodDecl &&
+          methodDecl->getDeclContext() == dc->getParentForLookup();
+
+        if (((!insideClass || !declaringMethod) &&
+             !options.is(TypeResolverContext::GenericRequirement)) ||
+            options.is(TypeResolverContext::ExplicitCastExpr)) {
+          Type SelfType = nominal->getSelfInterfaceType();
+          if (insideClass)
+            SelfType = DynamicSelfType::get(SelfType, ctx);
+          return resolution.mapTypeIntoContext(SelfType);
+        }
+
+        // Attempt to refer to 'Self' within a non-protocol nominal type.
         // Produce a Fix-It replacing 'Self' with the nominal type name.
         auto name = getDeclNameFromContext(dc, nominal);
         diags.diagnose(comp->getIdLoc(), diag::self_in_nominal, name)
diff --git a/test/decl/func/dynamic_self.swift b/test/decl/func/dynamic_self.swift
index 89c380b9de1d0..c76ef458c62dd 100644
--- a/test/decl/func/dynamic_self.swift
+++ b/test/decl/func/dynamic_self.swift
@@ -10,15 +10,15 @@ func inFunction() {
 }
 
 struct S0 {
-  func f() -> Self { } // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'S0'?}}{{15-19=S0}}
+  func f() -> Self { }
 
-  func g(_ ds: Self) { } // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'S0'?}}{{16-20=S0}}
+  func g(_ ds: Self) { }
 }
 
 enum E0 {
-  func f() -> Self { } // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'E0'?}}{{15-19=E0}}
+  func f() -> Self { }
 
-  func g(_ ds: Self) { } // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'E0'?}}{{16-20=E0}}
+  func g(_ ds: Self) { }
 }
 
 class C0 {
@@ -85,11 +85,11 @@ class C1 {
     var x: Int = self // expected-error{{cannot convert value of type 'Self.Type' to specified type 'Int'}}
 
     // Can't utter Self within the body of a method.
-    var c1 = C1(int: 5) as Self // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'C1'?}} {{28-32=C1}}
+    var c1 = C1(int: 5) as Self // expected-error{{'C1' is not convertible to 'Self'; did you mean to use 'as!' to force downcast?}}
 
     if b { return self.init(int: 5) }
 
-    return Self() // expected-error{{use of unresolved identifier 'Self'; did you mean 'self'?}}
+    return Self() // expected-error{{non-nominal type 'Self' does not support explicit initialization}}
   }
 
   // This used to crash because metatype construction went down a
@@ -412,4 +412,4 @@ class SelfOperator {
 func useSelfOperator() {
   let s = SelfOperator()
   _ = s + s
-}
\ No newline at end of file
+}
diff --git a/test/decl/nested/type_in_type.swift b/test/decl/nested/type_in_type.swift
index 6543b11344d78..6945639a0afda 100644
--- a/test/decl/nested/type_in_type.swift
+++ b/test/decl/nested/type_in_type.swift
@@ -417,7 +417,6 @@ extension OuterGeneric.MidNonGeneric {
   }
 
   func doMoreStuffWrong() -> Self {
-    // expected-error@-1 {{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'OuterGeneric.MidNonGeneric'?}}
 
   }
 }
diff --git a/test/type/self.swift b/test/type/self.swift
index 815842946a6ea..0a9fea9611bc8 100644
--- a/test/type/self.swift
+++ b/test/type/self.swift
@@ -1,7 +1,7 @@
 // RUN: %target-typecheck-verify-swift -swift-version 5
 
 struct S0<T> {
-  func foo(_ other: Self) { } // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'S0'?}}{{21-25=S0}}
+  func foo(_ other: Self) { }
 }
 
 class C0<T> {
@@ -9,7 +9,7 @@ class C0<T> {
 }
 
 enum E0<T> {
-  func foo(_ other: Self) { } // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'E0'?}}{{21-25=E0}}
+  func foo(_ other: Self) { }
 }
 
 // rdar://problem/21745221
@@ -23,7 +23,7 @@ extension X {
 }
 
 extension X.Inner {
-  func foo(_ other: Self) { } // expected-error{{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'X.Inner'?}}{{21-25=X.Inner}}
+  func foo(_ other: Self) { }
 }
 
 // SR-695
@@ -43,3 +43,111 @@ final class FinalMario : Mario {
     }
 }
 
+// These references to Self are now possible (SE-0068)
+
+class A<T> {
+  let b: Int
+  required init(a: Int) {
+    print("\(Self.self).\(#function)")
+    Self.y()
+    b = a
+  }
+  static func z(n: Self? = nil) {
+    // expected-error@-1 {{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'A'?}}
+    print("\(Self.self).\(#function)")
+  }
+  class func y() {
+    print("\(Self.self).\(#function)")
+    Self.z()
+  }
+  func x() -> A? {
+    print("\(Self.self).\(#function)")
+    Self.y()
+    Self.z()
+    let _: Self = Self.init(a: 66)
+    // expected-error@-1 {{'Self' is only available in a protocol or as the result of a method in a class; did you mean 'A'?}}
+    return Self.init(a: 77) as? Self as? A
+    // expected-warning@-1 {{conditional cast from 'Self' to 'Self' always succeeds}}
+    // expected-warning@-2 {{conditional downcast from 'Self?' to 'A<T>' is equivalent to an implicit conversion to an optional 'A<T>'}}
+  }
+}
+
+class B: A<Int> {
+  let a: Int
+  required convenience init(a: Int) {
+    print("\(Self.self).\(#function)")
+    self.init()
+  }
+  init() {
+    print("\(Self.self).\(#function)")
+    Self.y()
+    Self.z()
+    a = 99
+    super.init(a: 88)
+  }
+  override class func y() {
+    print("override \(Self.self).\(#function)")
+  }
+}
+
+class C {
+  required init() {
+  }
+  func f() {
+    func g(_: Self) {}
+  }
+  func g() {
+    _ = Self.init() as? Self
+    // expected-warning@-1 {{conditional cast from 'Self' to 'Self' always succeeds}}
+  }
+}
+
+struct S2 {
+  let x = 99
+  struct S3<T> {
+    let x = 99
+    static func x() {
+      Self.y()
+    }
+    func f() {
+      func g(_: Self) {}
+    }
+    static func y() {
+      print("HERE")
+    }
+    func foo(a: [Self]) -> Self? {
+      Self.x()
+      return Self.init() as? Self
+      // expected-warning@-1 {{conditional cast from 'S2.S3<T>' to 'S2.S3<T>' always succeeds}}
+    }
+  }
+}
+
+extension S2 {
+  static func x() {
+    Self.y()
+  }
+  static func y() {
+    print("HERE")
+  }
+  func f() {
+    func g(_: Self) {}
+  }
+  func foo(a: [Self]) -> Self? {
+    Self.x()
+    return Self.init() as? Self
+    // expected-warning@-1 {{conditional cast from 'S2' to 'S2' always succeeds}}
+  }
+}
+
+enum E {
+  static func f() {
+    func g(_: Self) {}
+    print("f()")
+  }
+  case e
+  func h(h: Self) -> Self {
+    Self.f()
+    return .e
+  }
+}