Wide bandgap semiconductors are ideal materials for the application of high power density, high frequency and low-loss power electronic devices, owning to the advantages of wide bandgap, high electron saturation velocity, and high breakdown field. Attributed to the high thermal conductivity, high chemical stability and high heat resistance of silicon carbide (SiC), epitaxy of wide bandgap semiconductors on SiC is promising to exploit the advantages of wide bandgap semiconductors and improve the performance of wide bandgap semiconductor devices. Benefiting from the continuous quality-improvement and cost-reduction of SiC substrates, wide bandgap semiconductors grown on SiC substrates are ushering in an explosive growth. Epitaxy of high quality wide bandgap semiconductors on SiC substrates is critical to the performance and reliability of wide bandgap semiconductor devices. This paper summarizes the recent progress obtained on epitaxial growth of SiC, gallium nitride (GaN) and gallium oxide (Ga2O3) on SiC substrates. In addition, the prospective of wide bandgap semiconductors grown on SiC substrates for high-performance electronics are prospected.