Electrical tuning of magnetism is of great fundamental and technical importance for fast, compact and ultra-low power electronic devices. Multiferroics, simultaneously exhibiting ferroelectricity and ferromagnetism, have attracted much interest owing to the capability of controlling magnetism by an electric field through magnetoelectric (ME) coupling. In particular, strong strain-mediated ME interaction observed in layered multiferroic heterostructures makes it practically possible for realizing electrically reconfigurable microwave devices, ultra-low power electronics and magnetoelectric random access memories (MERAMs). In this review, we demonstrate this remarkable E-field manipulation of magnetism in various multiferroic composite systems, aiming at the creation of novel compact, lightweight, energy-efficient and tunable electronic and microwave devices. First of all, tunable microwave devices are demonstrated based on ferrite/ferroelectric and magnetic-metal/ferroelectric composites, showing giant ferromagnetic resonance (FMR) tunability with narrow FMR linewidth. Then, E-field manipulation of magnetoresistance in multiferroic anisotropic magnetoresistance and giant magnetoresistance devices for achieving low-power electronic devices is discussed. Finally, E-field control of exchange-bias and deterministic magnetization switching is demonstrated in exchange-coupled antiferromagnetic/ferromagnetic/ferroelectric multiferroic hetero-structures at room temperature, indicating an important step towards MERAMs. In addition, recent progress in electrically non-volatile tuning of magnetic states is also presented. These tunable multiferroic heterostructures and devices provide great opportunities for next-generation reconfigurable radio frequency/microwave communication systems and radars, spintronics, sensors and memories.