Interference lithography at EUV and soft X-ray wavelengths: Principles, methods, and applications

•A review on interference lithography at EUV and soft X-ray wavelengths.•Achievements of groups in the field and their tool specifications and capabilities.•Description of XIL-II synchrotron beamline and the tabletop system at RWTH Aachen.•Applications are high-resolution patterning with EUV and Beyond EUV light.•Applications in Talbot lithography, tall nanostructure fabrication, and sensing.