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
@@ -250,6 +250,29 @@
   }
 };
 
+// `fir.load` --> `llvm.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();
+  }
+};
+
 /// conversion of fir::SelectRankOp to an if-then-else ladder
 struct SelectRankOpConversion : public FIROpConversion<fir::SelectRankOp> {
   using FIROpConversion::FIROpConversion;
@@ -262,7 +285,31 @@
   }
 };
 
-// convert to LLVM IR dialect `undef`
+/// `fir.store` --> `llvm.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;
 
@@ -275,7 +322,7 @@
   }
 };
 
-// convert to LLVM IR dialect `unreachable`
+/// `fir.unreachable` --> `llvm.unreachable`
 struct UnreachableOpConversion : public FIROpConversion<fir::UnreachableOp> {
   using FIROpConversion::FIROpConversion;
 
@@ -507,9 +554,9 @@
     pattern.insert<
         AddrOfOpConversion, CallOpConversion, ExtractValueOpConversion,
         HasValueOpConversion, GlobalOpConversion, InsertOnRangeOpConversion,
-        InsertValueOpConversion, SelectOpConversion, SelectRankOpConversion,
-        UndefOpConversion, UnreachableOpConversion, ZeroOpConversion>(
-        typeConverter);
+        InsertValueOpConversion, LoadOpConversion, SelectOpConversion,
+        SelectRankOpConversion, 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
@@ -376,3 +376,57 @@
 // CHECK-NEXT:    %0 = llvm.call @dummy_return_val() : () -> i32
 // CHECK-NEXT:    llvm.return %0 : i32
 // CHECK-NEXT:  }
+
+// -----
+
+// Test `fir.store` --> `llvm.store` conversion
+
+func @test_store_index(%val_to_store : index, %addr : !fir.ref<index>) {
+  fir.store %val_to_store to %addr : !fir.ref<index>
+  return
+}
+
+// CHECK-LABEL:   llvm.func @test_store_index
+// CHECK-SAME:    (%[[arg0:.*]]: i64, %[[arg1:.*]]: !llvm.ptr<i64>) {
+// CHECK-NEXT:    llvm.store %[[arg0]], %[[arg1]] : !llvm.ptr<i64>
+// CHECK-NEXT:    llvm.return
+// CHECK-NEXT:  }
+
+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
+}
+
+// CHECK-LABEL:  llvm.func @test_store_box
+// CHECK-SAME:  (%[[arg0:.*]]: !llvm.ptr<struct<(ptr<f{{.*}}>, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, array<2 x array<3 x i{{.*}}>>)>>,
+// CHECK-SAME:  %[[arg1:.*]]: !llvm.ptr<struct<(ptr<f{{.*}}>, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, array<2 x array<3 x i{{.*}}>>)>>) {
+// CHECK-NEXT:  %[[box_to_store:.*]] = llvm.load %arg1 : !llvm.ptr<struct<(ptr<f{{.*}}>, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, array<2 x array<3 x i{{.*}}>>)>>
+// CHECK-NEXT:  llvm.store %[[box_to_store]], %[[arg0]] : !llvm.ptr<struct<(ptr<f{{.*}}>, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, array<2 x array<3 x i{{.*}}>>)>>
+// CHECK-NEXT:  llvm.return
+// CHECK-NEXT:  }
+
+// -----
+
+// Test `fir.load` --> `llvm.load` conversion
+
+func @test_load_index(%addr : !fir.ref<index>) {
+  %0 = fir.load %addr : !fir.ref<index>
+  return
+}
+
+// CHECK-LABEL: llvm.func @test_load_index(
+// CHECK-SAME:  %[[arg1:.*]]: !llvm.ptr<i64>) {
+// CHECK-NEXT:    %0 = llvm.load %[[arg1]] : !llvm.ptr<i64>
+// CHECK-NEXT:    llvm.return
+// CHECK-NEXT:  }
+
+func @test_load_box(%addr : !fir.ref<!fir.box<!fir.array<10xf32>>>) {
+  %0 = fir.load %addr : !fir.ref<!fir.box<!fir.array<10xf32>>>
+  return
+}
+
+// Loading a `fir.ref<!fir.box>> is a no-op
+// CHECK-LABEL: llvm.func @test_load_box
+// CHECK-SAME: (%{{.*}}: !llvm.ptr<struct<(ptr<array<10 x f{{.*}}>>, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, i{{.*}}, array<1 x array<3 x i{{.*}}>>)>>) {
+// CHECK-NEXT:  llvm.return
+// CHECK-NEXT:  }