The electric-voltage-modulated magnetism in multiferroic heterostructures, also known as the converse magnetoelectric (ME) coupling, has drawn increasing research interest recently owing to its great potential applications in future low-power, high-speed electronic and/or spintronic devices, such as magnetic memory and computer logic. In this article, based on combined theoretical analysis and experimental demonstration, we investigate the film size dependence of such converse ME coupling in multiferroic magnetic/ferroelectric heterostructures, as well as exploring the interaction between two relating coupling mechanisms that are the interfacial strain and possibly the charge effects. We also briefly discuss some issues for the next step and describe new device prototypes that can be enabled by this technology.