diff --git a/flang/lib/Lower/OpenMP/OpenMP.cpp b/flang/lib/Lower/OpenMP/OpenMP.cpp
index 77786742b3e13..2cfc1bd88dcef 100644
--- a/flang/lib/Lower/OpenMP/OpenMP.cpp
+++ b/flang/lib/Lower/OpenMP/OpenMP.cpp
@@ -2192,6 +2192,21 @@ genTargetOp(lower::AbstractConverter &converter, lower::SymMap &symTable,
                            /*useDelayedPrivatization=*/true, symTable);
   dsp.processStep1(&clauseOps);
 
+  // Check if a value of type `type` can be passed to the kernel by value.
+  // All kernel parameters are of pointer type, so if the value can be
+  // represented inside of a pointer, then it can be passed by value.
+  auto isLiteralType = [&](mlir::Type type) {
+    const mlir::DataLayout &dl = firOpBuilder.getDataLayout();
+    mlir::Type ptrTy =
+        mlir::LLVM::LLVMPointerType::get(&converter.getMLIRContext());
+    uint64_t ptrSize = dl.getTypeSize(ptrTy);
+    uint64_t ptrAlign = dl.getTypePreferredAlignment(ptrTy);
+
+    auto [size, align] = fir::getTypeSizeAndAlignmentOrCrash(
+        loc, type, dl, converter.getKindMap());
+    return size <= ptrSize && align <= ptrAlign;
+  };
+
   // 5.8.1 Implicit Data-Mapping Attribute Rules
   // The following code follows the implicit data-mapping rules to map all the
   // symbols used inside the region that do not have explicit data-environment
@@ -2269,7 +2284,14 @@ genTargetOp(lower::AbstractConverter &converter, lower::SymMap &symTable,
           mapFlag |= llvm::omp::OpenMPOffloadMappingFlags::OMP_MAP_FROM;
         }
       } else if (fir::isa_trivial(eleType) || fir::isa_char(eleType)) {
-        captureKind = mlir::omp::VariableCaptureKind::ByCopy;
+        // Scalars behave as if they were "firstprivate".
+        // TODO: Handle objects that are shared/lastprivate or were listed
+        // in an in_reduction clause.
+        if (isLiteralType(eleType)) {
+          captureKind = mlir::omp::VariableCaptureKind::ByCopy;
+        } else {
+          mapFlag |= llvm::omp::OpenMPOffloadMappingFlags::OMP_MAP_TO;
+        }
       } else if (!fir::isa_builtin_cptr_type(eleType)) {
         mapFlag |= llvm::omp::OpenMPOffloadMappingFlags::OMP_MAP_TO;
         mapFlag |= llvm::omp::OpenMPOffloadMappingFlags::OMP_MAP_FROM;
diff --git a/flang/test/Lower/OpenMP/target-map-complex.f90 b/flang/test/Lower/OpenMP/target-map-complex.f90
new file mode 100644
index 0000000000000..c15a10e4804dd
--- /dev/null
+++ b/flang/test/Lower/OpenMP/target-map-complex.f90
@@ -0,0 +1,33 @@
+!RUN: %flang_fc1 -emit-hlfir -fopenmp %s -o - | FileCheck %s
+
+! Check that the complex*4 is passed by value. but complex*8 is passed by
+! reference
+
+!CHECK-LABEL: func.func @_QMmPbar()
+!CHECK:  %[[V0:[0-9]+]]:2 = hlfir.declare {{.*}} (!fir.ref<complex<f64>>) -> (!fir.ref<complex<f64>>, !fir.ref<complex<f64>>)
+!CHECK:  %[[V1:[0-9]+]]:2 = hlfir.declare {{.*}} (!fir.ref<complex<f32>>) -> (!fir.ref<complex<f32>>, !fir.ref<complex<f32>>)
+!CHECK:  %[[V2:[0-9]+]] = omp.map.info var_ptr(%[[V1]]#1 : !fir.ref<complex<f32>>, complex<f32>) {{.*}} capture(ByCopy)
+!CHECK:  %[[V3:[0-9]+]] = omp.map.info var_ptr(%[[V0]]#1 : !fir.ref<complex<f64>>, complex<f64>) {{.*}} capture(ByRef)
+!CHECK:  omp.target map_entries(%[[V2]] -> {{.*}}, %[[V3]] -> {{.*}} : !fir.ref<complex<f32>>, !fir.ref<complex<f64>>)
+
+module m
+  implicit none
+  complex(kind=4) :: cfval = (24, 25)
+  complex(kind=8) :: cdval = (28, 29)
+  interface
+    subroutine foo(x, y)
+      complex(kind=4) :: x
+      complex(kind=8) :: y
+      !$omp declare target
+    end
+  end interface
+
+contains
+
+subroutine bar()
+!$omp target
+    call foo(cfval, cdval)
+!$omp end target
+end
+
+end module
diff --git a/offload/test/offloading/fortran/target-map-literal-write.f90 b/offload/test/offloading/fortran/target-map-literal-write.f90
new file mode 100644
index 0000000000000..8f0cb95338eed
--- /dev/null
+++ b/offload/test/offloading/fortran/target-map-literal-write.f90
@@ -0,0 +1,20 @@
+!REQUIRES: flang, amdgpu
+
+!RUN: %libomptarget-compile-fortran-run-and-check-generic
+
+program m
+  complex(kind=8) :: x
+  x = (1.0, 2.0)
+!$omp target
+  x = (-1.0, -2.0)
+!$omp end target
+  print *, "x=", x
+end program
+
+! The host variable "x" should be passed to the kernel as "firstprivate",
+! hence the kernel should have its own copy of it. This is in contrast to
+! other cases where implicitly mapped variables have the TOFROM map-type.
+
+! Make sure that the target region didn't overwrite the host variable.
+
+!CHECK: x= (1.,2.)