The expanded compositional freedom afforded by high-entropy alloys (HEAs) represents a unique opportunity for the design of alloys for advanced nuclear applications, in particular for applications where current engineering alloys fall short. This review assesses the work done to date in the field of HEAs for nuclear applications, provides critical insight into the conclusions drawn, and highlights possibilities and challenges for future study. It is found that our understanding of the irradiation responses of HEAs remains in its infancy, and much work is needed in order for our knowledge of any single HEA system to match our understanding of conventional alloys such as austenitic steels. A number of studies have suggested that HEAs possess ‘special’ irradiation damage resistance, although some of the proposed mechanisms, such as those based on sluggish diffusion and lattice distortion, remain somewhat unconvincing (certainly in terms of being universally applicable to all HEAs). Nevertheless, there may be some mechanisms and effects that are uniquely different in HEAs when compared to more conventional alloys, such as the effect that their poor thermal conductivities have on the displacement cascade. Furthermore, the opportunity to tune the compositions of HEAs over a large range to optimise particular irradiation responses could be very powerful, even if the design process remains challenging