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The wide bandgap semiconductors SiC and GaN are commercialized for power electronics and for visible to UV light-emitting diodes in the case of the GaN/InGaN/AlGaN materials system. For power electronics applications, SiC MOSFETs (metal–oxide–semiconductor field effect transistors) and rectifiers and GaN/AlGaN HEMTs and vertical rectifiers provide more efficient switching at high-power levels than do Si devices and are now being used in electric vehicles and their charging infrastructure. These devices also have applications in more electric aircraft and space missions where high temperatures and extreme environments are involved. In this review, their inherent radiation hardness, defined as the tolerance to total doses, is compared to Si devices. This is higher for the wide bandgap semiconductors, due in part to their larger threshold energies for creating defects (atomic bond strength) and more importantly due to their high rates of defect recombination. However, it is now increasingly recognized that heavy-ion-induced catastrophic single-event burnout in SiC and GaN power devices commonly occurs at voltages ∼50% of the rated values. The onset of ion-induced leakage occurs above critical power dissipation within the epitaxial regions at high linear energy transfer rates and high applied biases. The amount of power dissipated along the ion track determines the extent of the leakage current degradation. The net result is the carriers produced along the ion track undergo impact ionization and thermal runaway. Light-emitting devices do not suffer from this mechanism since they are forward-biased. Strain has also recently been identified as a parameter that affects radiation susceptibility of the wide bandgap devices.