Multiferroic magnetoelectric composite systems such as ferromagnetic-ferroelectric heterostructures have recently attracted an ever-increasing interest and provoked a great number of research activities, driven by profound physics from coupling between ferroelectric and magnetic orders, as well as potential applications in novel multifunctional devices, such as sensors, transducers, memories, and spintronics. In this Review, we try to summarize what remarkable progress in multiferroic magnetoelectric composite systems has been achieved in most recent few years, with emphasis on thin films; and to describe unsolved issues and new device applications which can be controlled both electrically and magnetically.