In extreme radiation environments, such as space nuclear reactor systems, deep-space probe power modules, and launch vehicle propulsion systems, high-voltage and high-power devices demonstrate significant practical value. Silicon carbide (SiC) metal-oxide-semiconductor field-effect transistors (MOSFETs) possess advantages including high breakdown voltage, thermal stability, and low on-state resistance, enabling further improvements in aerospace power supply efficiency. Therefore, research on radiation effects and radiation-hardening techniques for SiC power MOSFETs has rapidly emerged as a critical focus in the industry. Firstly, this paper reviews the developmental evolution of SiC power MOSFETs, analyzes the necessity of transitioning from planar gate to trench-gate architectures, and provides future prospects for advanced SiC power MOSFET technologies. Secondly, it systematically compiles current research achievements in single event burnout (SEB) and single event gate rupture (SEGR) caused by heavy ion irradiation in SiC power MOSFETs. Finally, based on a mechanistic analysis of radiation-induced single event damage in SiC power MOSFETs, this study summarizes recent progress of radiation-hardening technologies, aiming to provide valuable ideas for understanding radiation induced failure mechanisms and enhancing the radiation tolerance of SiC power MOSFETs.