With the continuous development and progress of science and technology, the third-generation semiconductor power devices (SPDs) represented by SiC MOSFETs have become key devices in the field of power electronics due to their merits of excellent power density, high-temperature operating capability, high-frequency characteristics, and high-energy efficiency. However, when these devices are used in radiation environments like aviation and aerospace, significant challenges are posed to their reliability and performance. This article reviews the research on the core issues of radiation damage of SiC MOSFET power devices. It presents the research progress on the degradation mechanism, radiation damage mechanism, and radiation hardening technology of SiC MOSFET power devices under irradiation conditions of different types such as $\gamma $ -rays, electrons, protons, neutrons, and heavy ions. Hopefully, this review can provide an in-depth understanding of the reliability and stability of SiC MOSFET power devices in some special applications.