Wide-bandgap semiconductors exhibit much larger energy bandgaps than traditional semiconductors such as silicon, rendering them very promising to be applied in the fields of electronics and optoelectronics. Prominent examples of semiconductors include SiC, GaN, ZnO, and diamond, which exhibit distinctive characteristics such as elevated mobility and thermal conductivity. These characteristics facilitate the operation of a wide range of devices, including energy-efficient bipolar junction transistors (BJTs) and metal-oxide-semiconductor field-effect transistors (MOSFETs), as well as high-frequency high-electron-mobility transistors (HEMTs) and optoelectronic components such as light-emitting diodes (LEDs) and lasers. These semiconductors are used in building integrated circuits (ICs) to facilitate the operation of power electronics, computer devices, RF systems, and other optoelectronic advancements. These breakthroughs include various applications such as imaging, optical communication, and sensing. Among them, the field of power electronics has witnessed tremendous progress in recent years with the development of wide bandgap (WBG) semiconductor devices, which is capable of switching large currents and voltages rapidly with low losses. However, it has been proven challenging to integrate these devices with silicon complementary metal oxide semiconductor (CMOS) logic circuits required for complex control functions. The monolithic integration of silicon CMOS with WBG devices increases the complexity of fabricating monolithically integrated smart integrated circuits (ICs). This review article proposes implementing CMOS logic directly on the WBG platform as a solution. However, achieving the CMOS functionalities with the adoption of WBG materials still remains a significant hurdle. This article summarizes the research progress in the fabrication of integrated circuits adopting various WBG materials ranging from SiC to diamond, with the goal of building future smart power ICs.