In this review, recent achievements in the application of high-entropy alloys (HEAs) and high-entropy oxides (HEOs) in the technology of solid oxide fuel cells (SOFC) are discussed for the first time. The mechanisms of the stabilization of a high-entropy state in such materials, as well as the effect of structural and charge factors on the stability of the resulting homogeneous solid solution are performed. An introduction to the synthesis methods for HEAs and HEOs is given. The review highlights such advantages of high-entropy materials as high strength and the sluggish diffusion of components, which are promising for the use at the elevated temperatures, which are characteristic of SOFCs. Application of the medium- and high-entropy materials in the hydrocarbon-fueled SOFCs as protective layers for interconnectors and as anode components, caused by their high stability, are covered. High-entropy solid electrolytes are discussed in comparison with traditional electrolyte materials in terms of conductivity. High-entropy oxides are considered as prospective cathodes for SOFCs due to their superior electrochemical activity and long-term stability compared with the conventional perovskites. The present review also determines the prioritizing directions in the future development of high-entropy materials as electrolytes and electrodes for SOFCs operating in the intermediate and low temperature ranges.