The expansion of the electric vehicle market is driving the request for efficient and reliable power electronic systems for electric energy conversion and processing. The efficiency, size, and cost of a power system is strongly related to the performance of power semiconductor devices, where massive industrial investments and intense research efforts are being devoted to new wide bandgap (WBG) semiconductors, such as silicon carbide (SiC) and gallium nitride (GaN). The electrical and thermal properties of SiC and GaN enable the fabrication of semiconductor power devices with performance well beyond the limits of silicon. However, a massive migration of the power electronics industry towards WBG materials can be obtained only once the corresponding fabrication technology reaches a sufficient maturity and a competitive cost. In this paper, we present a perspective of power electronics based on WBG semiconductors, from fundamental material characteristics of SiC and GaN to their potential impacts on the power semiconductor device market. Some application cases are also presented, with specific benchmarks against a corresponding implementation realized with silicon devices, focusing on both achievable performance and system cost.