The development of microelectronics is always driven by reducing transistor size and increasing integration, from the initial micron-scale to the current few nanometers. The photolithography technique for manufacturing the transistor needs to reduce the wavelength of the optical wave, from ultraviolet, deep, to the existing extreme ultraviolet light. One approach toward decreasing the working wavelength is using lithography based on beyond extreme ultraviolet radiation (BEUV) with a wavelength around 7 nm. The BEUV lithography relies on advanced reflective optics such as periodic multilayer film X-ray mirrors (PMMs). PMMs are artificial Bragg crystals having alternate layers of “light” and “heavy” materials. The periodicity of such a structure is relatively half of the working wavelength. Since a BEUV lithographical system contains at least 10 mirrors, optics’ reflectivity becomes a crucial point. The increasing of a single mirror's reflectivity by 10% will increase the system’s overall throughput by 6 times. In this work, the properties and development status of PMMs, particularly for BEUV lithography, were reviewed to gain a better understanding of their advantages and limitations. Emphasis was given to materials, design concepts, structure, deposition method, and optical characteristics of these coatings.