Multiferroic heterostructures can be synthesized by integrating monolithic ferroelectric and magnetic materials with interfacial coupling between electric polarization and magnetization, through the exchange of elastic, electric, and magnetic energy. Although the nature of the interfaces remains to be unraveled, such cross coupling can be utilized to manipulate the magnetization (or polarization) with an electric (or magnetic) field, known as a converse (or direct) magnetoelectric effect. It can be exploited to significantly improve the performance of or/and add new functionalities to many existing or emerging devices such as memory devices, tunable microwave devices, sensors, etc. The exciting technological potential, along with the rich physical phenomena at the interface, has sparked intensive research on multiferroic heterostructures for more than a decade. Here, we summarize the most recent progresses in the fundamental principles and potential applications of the interface-based magnetoelectric effect in multiferroic heterostructures, and present our perspectives on some key issues that require further study in order to realize their practical device applications.