Over the past few years, interest in high-entropic alloys (HEAs) has been growing. A large body of research has been undertaken to study aspects such as the microstructure features of HEAs of various compositions, the effect of the content of certain elements on the mechanical properties of HEAs, and, of course, special properties such as heat resistance, corrosion resistance, resistance to irradiation with high-energy particles, magnetic properties, etc. However, few works have presented results accumulated over several years, which can complicate the choice of directions for further research. This review article presents the results of studies of the mechanisms of high-temperature oxidation of HEAs of systems: Al-Co-Cr-Fe-Ni, Mn-Co-Cr-Fe-Ni, refractory HEAs. An analysis made it possible to systematize the features of high-temperature oxidation of HEAs and propose new directions for the development of heat-resistant HEAs. The presented information may be useful for assessing the possibility of the practical application of HEAs in the aerospace industry, in nuclear and chemical engineering, and in new areas of energy.