A new class of metallic materials, so-called “high-entropy alloys” (HEAs), was under review. Various definitions of these alloys are given, their main differences from the conventional alloys are indicated and the dynamics of publications in the period from the first publications in 2004 to the end of 2020 are presented. It is noted the almost exponential growth of the article numbers concerning these alloys, and the main reasons of such high interest are discussed. Experimental results of development the radiation-tolerant materials based on the concept of high-entropy alloys and study of the radiation damage mechanisms are summarised.