Multiferroic magnetoelectric nanostructures with coupled magnetization and electric polarization across their interfaces have stimulated intense research activities over the past decade. Such interface-based magnetoelectric coupling can be exploited to significantly improve the performance of many devices such as memories, tunable radio-frequency/microwave devices, and magnetic sensors. In this article, we introduce a number of current or developing technologies and discuss their limitations. We describe how the use of magnetoelectric nanostructures can overcome these limitations to optimize device performance. We also present challenges that need to be addressed in pursuing practical applications of magnetoelectric devices.