High-entropy alloys (HEAs), based on equiatomic or near-equiatomic mixture of usually four or more elements, have attracted considerable attention as there are indications that along with surprising microstructural simplicity of some alloys, they may also offer intriguing combinations of mechanical and other properties. Amongst these properties, there is growing interest in the irradiation response of HEAs and their potential to withstand the neutron bombardment environment of future civil nuclear power plants. One of the first proposed HEAs is face-centred cubic CrMnFeCoNi, also known as the Cantor alloy, and the irradiation response of the Cantor alloy and its sub-systems are the focus of this review. Using irradiation analogues (electrons, heavy ions and He) to neutron bombardment and considering simulations, advanced microstructural analysis and property measurement, the Cantor alloy and its derivatives are shown to exhibit encouraging irradiation resistance that, in many instances, is superior to more traditional dilute alloys of the same elements. The beneficial aspects are high phase stability and resistance to radiation-induced segregation, smaller size but higher number density of dislocation loops, significantly lower extent of swelling and improved resistance to He bubble growth. The future research directions for irradiation resistant HEAs are also suggested.