The multilayer mirrors in the extreme ultraviolet region have significantly advanced various scientific and technological fields, including extreme ultraviolet lithography, astrophysics, plasma diagnosis, attophysics, and free electron lasers. These multilayer coatings are crucial for developing mirrors that achieve high reflectivity and narrow bandwidth at normal incidence within the extreme ultraviolet spectrum. Multilayer mirrors are now key components in both imaging and spectroscopy across various applications. Optical imaging systems equipped with multilayer mirrors have conducted numerous solar observations in different emission lines, achieving unprecedented spatial and spectral resolutions. This paper reviews the progress of the most promising multilayer mirrors, covering the 40 nm to 90 nm range. Following a brief introduction to multilayer theory, it highlights the most promising material pairs and layer stack structures based on Mg, Sc, and lanthanides. The review emphasizes multilayer mirrors that exhibit high reflectivity within the 40 nm to 90 nm wavelength range and discusses their temporal stability.