With significant recent progress in the thin film deposition and nanofabrication technology, a number of physical phenomena occur at the interfaces of magnetic thin films, and their heterostructures have been discovered. Consequently, the electric field-induced modulation of those interfacial properties mediated through spin–orbit coupling promises to develop magnetic material based smarter, faster, miniaturized, energy efficient spintronic devices. Among them, the electric field-induced modification of interfacial magnetic anisotropy, popularly termed as voltage-controlled magnetic anisotropy (VCMA), has attracted special attention because of its salient features. This article is devoted to reviewing the recent development of magnonics, which deals with collective precessional motion of ordered magnetic spins, i.e., spin waves (SWs), and skyrmions with chiral spin textures, with VCMA, including the perspectives of this research field. Starting with a broad introduction, the key features of VCMA and its advantages over other electric field-induced methods are highlighted. These are followed by describing the state-of-the-art of VCMA, and various other direct and indirect electric field-induced methods for magnetization reversal; controlling skyrmion dynamics; excitation, manipulation, and channeling of SWs; and tailoring magnonic bands. The critical challenges, their possible solutions, and future perspectives of this field are thoroughly discussed throughout the article.