The article provides a review of the current state of affairs in the field of physics and technology of multilayer beryllium-containing mirrors intended for projection lithography and solar corona studies in the extreme ultraviolet (EUV) range. The methods of synthesizing and studying beryllium-containing multilayer mirrors are described. The results of recent studies of the internal structure and EUV reflection coefficients are given for Mo/Be, Mo/Si, Be/Al, and Be/Mg multilayer mirrors. The effect of the Si and Be interlayers on the reflectivity is explained. The directions for further research on beryllium-containing mirrors are discussed.