diff --git a/flang/lib/Optimizer/CodeGen/CodeGen.cpp b/flang/lib/Optimizer/CodeGen/CodeGen.cpp
--- a/flang/lib/Optimizer/CodeGen/CodeGen.cpp
+++ b/flang/lib/Optimizer/CodeGen/CodeGen.cpp
@@ -19,6 +19,7 @@
 #include "mlir/Conversion/LLVMCommon/TypeConverter.h"
 #include "mlir/Conversion/StandardToLLVM/ConvertStandardToLLVM.h"
 #include "mlir/IR/BuiltinTypes.h"
+#include "mlir/IR/Location.h"
 #include "mlir/Pass/Pass.h"
 #include "llvm/ADT/ArrayRef.h"
 
@@ -154,6 +155,53 @@
   }
 };
 
+// convert to LLVM IR dialect `load`
+struct LoadOpConversion : public FIROpConversion<fir::LoadOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::LoadOp load, OpAdaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    // fir.box is a special case because it is considered as an ssa values in
+    // fir, but it is lowered as a pointer to a descriptor. So fir.ref<fir.box>
+    // and fir.box end up being the same llvm types and loading a
+    // fir.ref<fir.box> is actually a no op in LLVM.
+    if (load.getType().isa<fir::BoxType>()) {
+      rewriter.replaceOp(load, adaptor.getOperands()[0]);
+    } else {
+      mlir::Type ty = convertType(load.getType());
+      ArrayRef<NamedAttribute> at = load->getAttrs();
+      rewriter.replaceOpWithNewOp<mlir::LLVM::LoadOp>(load, ty,
+          adaptor.getOperands(), at);
+    }
+    return success();
+  }
+};
+
+// convert to LLVM IR dialect `store`
+struct StoreOpConversion : public FIROpConversion<fir::StoreOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::StoreOp store, OpAdaptor adaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    if (store.value().getType().isa<fir::BoxType>()) {
+      // fir.box value is actually in memory, load it first before storing it.
+      mlir::Location loc = store.getLoc();
+      mlir::Type boxPtrTy = adaptor.getOperands()[0].getType();
+      auto val = rewriter.create<mlir::LLVM::LoadOp>(
+          loc, boxPtrTy.cast<mlir::LLVM::LLVMPointerType>().getElementType(),
+          adaptor.getOperands()[0]);
+      rewriter.replaceOpWithNewOp<mlir::LLVM::StoreOp>(
+          store, val, adaptor.getOperands()[1]);
+    } else {
+      rewriter.replaceOpWithNewOp<mlir::LLVM::StoreOp>(
+          store, adaptor.getOperands()[0], adaptor.getOperands()[1]);
+    }
+    return success();
+  }
+};
+
 // convert to LLVM IR dialect `undef`
 struct UndefOpConversion : public FIROpConversion<fir::UndefOp> {
   using FIROpConversion::FIROpConversion;
@@ -220,10 +268,9 @@
     auto *context = getModule().getContext();
     fir::LLVMTypeConverter typeConverter{getModule()};
     mlir::OwningRewritePatternList pattern(context);
-    pattern
-        .insert<AddrOfOpConversion, HasValueOpConversion, GlobalOpConversion,
-                UndefOpConversion, UnreachableOpConversion, ZeroOpConversion>(
-            typeConverter);
+    pattern.insert<AddrOfOpConversion, HasValueOpConversion, GlobalOpConversion,
+                   LoadOpConversion, StoreOpConversion, UndefOpConversion,
+                   UnreachableOpConversion, ZeroOpConversion>(typeConverter);
     mlir::populateStdToLLVMConversionPatterns(typeConverter, pattern);
     mlir::arith::populateArithmeticToLLVMConversionPatterns(typeConverter,
                                                             pattern);
diff --git a/flang/test/Fir/convert-to-llvm.fir b/flang/test/Fir/convert-to-llvm.fir
--- a/flang/test/Fir/convert-to-llvm.fir
+++ b/flang/test/Fir/convert-to-llvm.fir
@@ -145,3 +145,40 @@
 func @test_unreachable() {
   fir.unreachable
 }
+
+// -----
+
+// Verify that fir.store is transformed to llvm.store
+
+// CHECK:  llvm.func @test_store() {
+// CHECK-NEXT:    llvm.store
+// CHECK-NEXT:    llvm.return
+// CHECK-NEXT:  }
+
+func @test.store(%lb : index, %addr : !fir.ref<index>) {
+  fir.store %lb to %addr : !fir.ref<index>
+  return
+}
+
+// TODO Add a test with fir.ref<fir.box> once we have more support for fir.box,
+// e.g.
+// func @test_store_box(%array : !fir.ref<!fir.box<!fir.array<?x?xf32>>>, %box : !fir.box<!fir.array<?x?xf32>>) {
+//   fir.store %box to %array : !fir.ref<!fir.box<!fir.array<?x?xf32>>>
+//   return
+// }
+
+// -----
+
+// Verify that fir.load is transformed to llvm.load
+
+// CHECK:  llvm.func @test_load() {
+// CHECK-NEXT:    %{{.*}} = llvm.load
+// CHECK-NEXT:    llvm.return
+// CHECK-NEXT:  }
+
+func @test_load(%lb : index, %addr : !fir.ref<index>) {
+  %1 = fir.load %addr : !fir.ref<index>
+  return
+}
+
+// TODO Add a test with fir.ref<fir.box> once we have more support for fir.box