diff --git a/mlir/include/mlir-c/Pass.h b/mlir/include/mlir-c/Pass.h
--- a/mlir/include/mlir-c/Pass.h
+++ b/mlir/include/mlir-c/Pass.h
@@ -70,9 +70,9 @@
 MLIR_CAPI_EXPORTED MlirOpPassManager
 mlirPassManagerGetAsOpPassManager(MlirPassManager passManager);
 
-/// Run the provided `passManager` on the given `module`.
+/// Run the provided `passManager` on the given `op`.
 MLIR_CAPI_EXPORTED MlirLogicalResult
-mlirPassManagerRun(MlirPassManager passManager, MlirModule module);
+mlirPassManagerRunOnOp(MlirPassManager passManager, MlirOperation op);
 
 /// Enable mlir-print-ir-after-all.
 MLIR_CAPI_EXPORTED void
diff --git a/mlir/lib/Bindings/Python/Pass.cpp b/mlir/lib/Bindings/Python/Pass.cpp
--- a/mlir/lib/Bindings/Python/Pass.cpp
+++ b/mlir/lib/Bindings/Python/Pass.cpp
@@ -117,8 +117,8 @@
       .def(
           "run",
           [](PyPassManager &passManager, PyModule &module) {
-            MlirLogicalResult status =
-                mlirPassManagerRun(passManager.get(), module.get());
+            MlirLogicalResult status = mlirPassManagerRunOnOp(
+                passManager.get(), mlirModuleGetOperation(module.get()));
             if (mlirLogicalResultIsFailure(status))
               throw SetPyError(PyExc_RuntimeError,
                                "Failure while executing pass pipeline.");
diff --git a/mlir/lib/CAPI/IR/Pass.cpp b/mlir/lib/CAPI/IR/Pass.cpp
--- a/mlir/lib/CAPI/IR/Pass.cpp
+++ b/mlir/lib/CAPI/IR/Pass.cpp
@@ -39,9 +39,9 @@
   return wrap(static_cast<OpPassManager *>(unwrap(passManager)));
 }
 
-MlirLogicalResult mlirPassManagerRun(MlirPassManager passManager,
-                                     MlirModule module) {
-  return wrap(unwrap(passManager)->run(unwrap(module)));
+MlirLogicalResult mlirPassManagerRunOnOp(MlirPassManager passManager,
+                                         MlirOperation op) {
+  return wrap(unwrap(passManager)->run(unwrap(op)));
 }
 
 void mlirPassManagerEnableIRPrinting(MlirPassManager passManager) {
diff --git a/mlir/test/CAPI/execution_engine.c b/mlir/test/CAPI/execution_engine.c
--- a/mlir/test/CAPI/execution_engine.c
+++ b/mlir/test/CAPI/execution_engine.c
@@ -37,7 +37,8 @@
   mlirPassManagerAddOwnedPass(pm, mlirCreateConversionConvertFuncToLLVMPass());
   mlirOpPassManagerAddOwnedPass(
       opm, mlirCreateConversionArithToLLVMConversionPass());
-  MlirLogicalResult status = mlirPassManagerRun(pm, module);
+  MlirLogicalResult status =
+      mlirPassManagerRunOnOp(pm, mlirModuleGetOperation(module));
   if (mlirLogicalResultIsFailure(status)) {
     fprintf(stderr, "Unexpected failure running pass pipeline\n");
     exit(2);
diff --git a/mlir/test/CAPI/pass.c b/mlir/test/CAPI/pass.c
--- a/mlir/test/CAPI/pass.c
+++ b/mlir/test/CAPI/pass.c
@@ -33,17 +33,16 @@
   MlirContext ctx = mlirContextCreate();
   registerAllUpstreamDialects(ctx);
 
-  MlirModule module = mlirModuleCreateParse(
-      ctx,
-      // clang-format off
-                            mlirStringRefCreateFromCString(
-"func.func @foo(%arg0 : i32) -> i32 {                                   \n"
-"  %res = arith.addi %arg0, %arg0 : i32                                     \n"
-"  return %res : i32                                                        \n"
-"}"));
-  // clang-format on
-  if (mlirModuleIsNull(module)) {
-    fprintf(stderr, "Unexpected failure parsing module.\n");
+  const char *funcAsm = //
+      "func.func @foo(%arg0 : i32) -> i32 {   \n"
+      "  %res = arith.addi %arg0, %arg0 : i32 \n"
+      "  return %res : i32                    \n"
+      "}                                      \n";
+  MlirOperation func =
+      mlirOperationCreateParse(ctx, mlirStringRefCreateFromCString(funcAsm),
+                               mlirStringRefCreateFromCString("funcAsm"));
+  if (mlirOperationIsNull(func)) {
+    fprintf(stderr, "Unexpected failure parsing asm.\n");
     exit(EXIT_FAILURE);
   }
 
@@ -56,14 +55,14 @@
     MlirPassManager pm = mlirPassManagerCreate(ctx);
     MlirPass printOpStatPass = mlirCreateTransformsPrintOpStats();
     mlirPassManagerAddOwnedPass(pm, printOpStatPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, func);
     if (mlirLogicalResultIsFailure(success)) {
       fprintf(stderr, "Unexpected failure running pass manager.\n");
       exit(EXIT_FAILURE);
     }
     mlirPassManagerDestroy(pm);
   }
-  mlirModuleDestroy(module);
+  mlirOperationDestroy(func);
   mlirContextDestroy(ctx);
 }
 
@@ -71,22 +70,23 @@
   MlirContext ctx = mlirContextCreate();
   registerAllUpstreamDialects(ctx);
 
-  MlirModule module = mlirModuleCreateParse(
-      ctx,
-      // clang-format off
-                            mlirStringRefCreateFromCString(
-"func.func @foo(%arg0 : i32) -> i32 {                                   \n"
-"  %res = arith.addi %arg0, %arg0 : i32                                     \n"
-"  return %res : i32                                                        \n"
-"}                                                                          \n"
-"module {                                                                   \n"
-"  func.func @bar(%arg0 : f32) -> f32 {                                     \n"
-"    %res = arith.addf %arg0, %arg0 : f32                                   \n"
-"    return %res : f32                                                      \n"
-"  }                                                                        \n"
-"}"));
-  // clang-format on
-  if (mlirModuleIsNull(module))
+  const char *moduleAsm = //
+      "module {                                   \n"
+      "  func.func @foo(%arg0 : i32) -> i32 {     \n"
+      "    %res = arith.addi %arg0, %arg0 : i32   \n"
+      "    return %res : i32                      \n"
+      "  }                                        \n"
+      "  module {                                 \n"
+      "    func.func @bar(%arg0 : f32) -> f32 {   \n"
+      "      %res = arith.addf %arg0, %arg0 : f32 \n"
+      "      return %res : f32                    \n"
+      "    }                                      \n"
+      "  }                                        \n"
+      "}                                          \n";
+  MlirOperation module =
+      mlirOperationCreateParse(ctx, mlirStringRefCreateFromCString(moduleAsm),
+                               mlirStringRefCreateFromCString("moduleAsm"));
+  if (mlirOperationIsNull(module))
     exit(1);
 
   // Run the print-op-stats pass on functions under the top-level module:
@@ -100,7 +100,7 @@
         pm, mlirStringRefCreateFromCString("func.func"));
     MlirPass printOpStatPass = mlirCreateTransformsPrintOpStats();
     mlirOpPassManagerAddOwnedPass(nestedFuncPm, printOpStatPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, module);
     if (mlirLogicalResultIsFailure(success))
       exit(2);
     mlirPassManagerDestroy(pm);
@@ -118,13 +118,13 @@
         nestedModulePm, mlirStringRefCreateFromCString("func.func"));
     MlirPass printOpStatPass = mlirCreateTransformsPrintOpStats();
     mlirOpPassManagerAddOwnedPass(nestedFuncPm, printOpStatPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, module);
     if (mlirLogicalResultIsFailure(success))
       exit(2);
     mlirPassManagerDestroy(pm);
   }
 
-  mlirModuleDestroy(module);
+  mlirOperationDestroy(module);
   mlirContextDestroy(ctx);
 }
 
@@ -339,16 +339,17 @@
   MlirContext ctx = mlirContextCreate();
   registerAllUpstreamDialects(ctx);
 
-  MlirModule module = mlirModuleCreateParse(
-      ctx,
-      // clang-format off
-      mlirStringRefCreateFromCString(
-"func.func @foo(%arg0 : i32) -> i32 {                                   \n"
-"  %res = arith.addi %arg0, %arg0 : i32                                     \n"
-"  return %res : i32                                                        \n"
-"}"));
-  // clang-format on
-  if (mlirModuleIsNull(module)) {
+  const char *moduleAsm = //
+      "module {                                 \n"
+      "  func.func @foo(%arg0 : i32) -> i32 {   \n"
+      "    %res = arith.addi %arg0, %arg0 : i32 \n"
+      "    return %res : i32                    \n"
+      "  }                                      \n"
+      "}";
+  MlirOperation module =
+      mlirOperationCreateParse(ctx, mlirStringRefCreateFromCString(moduleAsm),
+                               mlirStringRefCreateFromCString("moduleAsm"));
+  if (mlirOperationIsNull(module)) {
     fprintf(stderr, "Unexpected failure parsing module.\n");
     exit(EXIT_FAILURE);
   }
@@ -377,7 +378,7 @@
 
     MlirPassManager pm = mlirPassManagerCreate(ctx);
     mlirPassManagerAddOwnedPass(pm, externalPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, module);
     if (mlirLogicalResultIsFailure(success)) {
       fprintf(stderr, "Unexpected failure running external pass.\n");
       exit(EXIT_FAILURE);
@@ -421,7 +422,7 @@
     MlirOpPassManager nestedFuncPm =
         mlirPassManagerGetNestedUnder(pm, funcOpName);
     mlirOpPassManagerAddOwnedPass(nestedFuncPm, externalPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, module);
     if (mlirLogicalResultIsFailure(success)) {
       fprintf(stderr, "Unexpected failure running external operation pass.\n");
       exit(EXIT_FAILURE);
@@ -469,7 +470,7 @@
 
     MlirPassManager pm = mlirPassManagerCreate(ctx);
     mlirPassManagerAddOwnedPass(pm, externalPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, module);
     if (mlirLogicalResultIsFailure(success)) {
       fprintf(stderr, "Unexpected failure running external pass.\n");
       exit(EXIT_FAILURE);
@@ -516,7 +517,7 @@
 
     MlirPassManager pm = mlirPassManagerCreate(ctx);
     mlirPassManagerAddOwnedPass(pm, externalPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, module);
     if (mlirLogicalResultIsSuccess(success)) {
       fprintf(
           stderr,
@@ -564,7 +565,7 @@
 
     MlirPassManager pm = mlirPassManagerCreate(ctx);
     mlirPassManagerAddOwnedPass(pm, externalPass);
-    MlirLogicalResult success = mlirPassManagerRun(pm, module);
+    MlirLogicalResult success = mlirPassManagerRunOnOp(pm, module);
     if (mlirLogicalResultIsSuccess(success)) {
       fprintf(
           stderr,
@@ -587,7 +588,7 @@
   }
 
   mlirTypeIDAllocatorDestroy(typeIDAllocator);
-  mlirModuleDestroy(module);
+  mlirOperationDestroy(module);
   mlirContextDestroy(ctx);
 }