Progress in the field of reflective multilayer coatings for the wavelength region between 50 Å and 2000 Å is reviewed. All the coatings contain absorbing materials, absorption losses are minimized by positioning strongly absorbing materials into the nodes of the standing wave inside the coating. Above λ=1200 Å, ideal coatings with a reflectivity approaching 100% are theoretically possible. The theoretical predictions have been confirmed for coatings up to six layers at wavelengths around 2000 Å. Below λ=1000 Å, no Absorption- Free material is available that can be used as a spacer layer to cover the antinodes of the standing wave field. This limits the theoretically obtainable reflectivity: However, even at the shortest wavelength a reflectivity of 30% is still possible. Experimental results have been obtained for wavelengths between 100 Å and 200 Å for coatings up to nine layers. Discrepancies between experiment and theory can be explained as due to insufficient knowledge of the optical constants of the films used. Extensive future work on the optical constants of materials and their dependence on film thickness and deposition conditions is required for further improvement. © 1976 Optical Society of America.