Index: lib/Sema/SemaDecl.cpp
===================================================================
--- lib/Sema/SemaDecl.cpp
+++ lib/Sema/SemaDecl.cpp
@@ -16308,6 +16308,15 @@
   TU->setModuleOwnershipKind(Decl::ModuleOwnershipKind::ModulePrivate);
   TU->setLocalOwningModule(Mod);
 
+  // Modules TS + p0731r0 [dcl.module.interface]p1:
+  //   Every name of an entity with linkage other than internal linkage made
+  //   visible in the purview of the module interface unit of a module M is
+  //   visible in the purview of all module implementation units of M.
+  if (MDK == ModuleDeclKind::Implementation) {
+    for (Module *ImportedModule : Mod->Imports)
+      VisibleModules.setVisible(ImportedModule, ModuleLoc);
+  }
+
   // FIXME: Create a ModuleDecl.
   return nullptr;
 }
@@ -16355,10 +16364,19 @@
     Context.addModuleInitializer(ModuleScopes.back().Module, Import);
   CurContext->addDecl(Import);
 
-  // Re-export the module if needed.
-  if (Import->isExported() &&
-      !ModuleScopes.empty() && ModuleScopes.back().ModuleInterface)
-    getCurrentModule()->Exports.emplace_back(Mod, false);
+  if (getLangOpts().ModulesTS &&
+      !ModuleScopes.empty() && ModuleScopes.back().ModuleInterface) {
+    Module *CurrentModule = getCurrentModule();
+
+    // Store imports that occur in the purview of a module interface unit.
+    // This is so that we know what to make visible in the purview of the
+    // corresponding implementation units.
+    CurrentModule->Imports.insert(Mod);
+
+    // Re-export the module if needed.
+    if (Import->isExported())
+      CurrentModule->Exports.emplace_back(Mod, false);
+  }
 
   return Import;
 }
Index: test/CXX/modules-ts/basic/basic.def.odr/p6/module-vs-module.cpp
===================================================================
--- test/CXX/modules-ts/basic/basic.def.odr/p6/module-vs-module.cpp
+++ test/CXX/modules-ts/basic/basic.def.odr/p6/module-vs-module.cpp
@@ -10,9 +10,7 @@
 //
 // RUN: %clang_cc1 -fmodules-ts -std=c++17 %s -fmodule-file=%t/M.pcm -emit-module-interface -o %t/N.pcm -DMODULE_INTERFACE -DNO_ERRORS
 // RUN: %clang_cc1 -fmodules-ts -std=c++17 %s -fmodule-file=%t/N.pcm -verify
-// FIXME: Once we start importing "import" declarations properly, this should
-// be rejected (-verify should be added to the following line).
-// RUN: %clang_cc1 -fmodules-ts -std=c++17 %s -fmodule-file=%t/N.pcm -DNO_IMPORT
+// RUN: %clang_cc1 -fmodules-ts -std=c++17 %s -fmodule-file=%t/N.pcm -DNO_IMPORT -verify
 //
 // RUN: %clang_cc1 -fmodules-ts -std=c++17 %s -fmodule-file=%t/M.pcm -emit-module-interface -o %t/N-no-M.pcm -DMODULE_INTERFACE -DNO_ERRORS -DNO_IMPORT
 // RUN: %clang_cc1 -fmodules-ts -std=c++17 %s -fmodule-file=%t/N-no-M.pcm -verify
Index: test/CXX/modules-ts/dcl.dcl/dcl.module/dcl.module.interface/p1.cpp
===================================================================
--- test/CXX/modules-ts/dcl.dcl/dcl.module/dcl.module.interface/p1.cpp
+++ test/CXX/modules-ts/dcl.dcl/dcl.module/dcl.module.interface/p1.cpp
@@ -1,28 +0,0 @@
-// RUN: %clang_cc1 -fmodules-ts %s -verify -o /dev/null
-// RUN: %clang_cc1 -fmodules-ts %s -DINTERFACE -verify -emit-module-interface -o %t
-// RUN: %clang_cc1 -fmodules-ts %s -DIMPLEMENTATION -verify -fmodule-file=%t -o /dev/null
-//
-// RUN: %clang_cc1 -fmodules-ts %s -DBUILT_AS_INTERFACE -emit-module-interface -verify -o /dev/null
-// RUN: %clang_cc1 -fmodules-ts %s -DINTERFACE -DBUILT_AS_INTERFACE -emit-module-interface -verify -o /dev/null
-// RUN: %clang_cc1 -fmodules-ts %s -DIMPLEMENTATION -DBUILT_AS_INTERFACE -emit-module-interface -verify -o /dev/null
-
-#if INTERFACE
-// expected-no-diagnostics
-export module A;
-#elif IMPLEMENTATION
-module A;
- #ifdef BUILT_AS_INTERFACE
-  // expected-error@-2 {{missing 'export' specifier in module declaration while building module interface}}
-  #define INTERFACE
- #endif
-#else
- #ifdef BUILT_AS_INTERFACE
-  // expected-error@1 {{missing 'export module' declaration in module interface unit}}
- #endif
-#endif
-
-#ifndef INTERFACE
-export int b; // expected-error {{export declaration can only be used within a module interface unit}}
-#else
-export int a;
-#endif
Index: test/CXX/modules-ts/dcl.dcl/dcl.module/dcl.module.interface/p1/interface-imports.cpp
===================================================================
--- test/CXX/modules-ts/dcl.dcl/dcl.module/dcl.module.interface/p1/interface-imports.cpp
+++ test/CXX/modules-ts/dcl.dcl/dcl.module/dcl.module.interface/p1/interface-imports.cpp
@@ -0,0 +1,29 @@
+// RUN: rm -rf %t
+// RUN: mkdir -p %t
+// RUN: echo 'export module a; export class A { };' > %t/a.cppm
+// RUN: echo 'export module b; export class B { };' > %t/b.cppm
+//
+// RUN: %clang_cc1 -fmodules-ts -emit-module-interface %t/a.cppm -o %t/a.pcm
+// RUN: %clang_cc1 -fmodules-ts -emit-module-interface %t/b.cppm -o %t/b.pcm
+//
+// RUN: %clang_cc1 -fmodules-ts -fprebuilt-module-path=%t -emit-module-interface %s -o %t/test.pcm -DINTERFACE
+// RUN: %clang_cc1 -fmodules-ts -I%t -fmodule-file=%t/test.pcm %s -verify
+
+#ifdef INTERFACE
+
+import a;
+export module test;
+import b;
+
+#else // IMPLEMENTATION
+
+module test;
+
+A a; // expected-error {{must be imported from module 'a'}}
+     // expected-note@a.cppm:1 {{here}}
+
+// Module b is imported within the purview of this module's interface unit.
+// So its exported definitions should be visible here.
+B b;
+
+#endif