Extreme Ultraviolet Lithography (EUVL) is will soon be fully practically applicable to the high volume manufacture of semiconductor chips. This paper describes the establishment of soft X-ray or EUV optical technology utilizing multilayer optical elements and the early stages of research regarding its application as a lithographic technique. The technology was established through the demonstration of three fundamental properties of optics: imaging, interference, and polarization in the soft X-ray region by multilayer optical elements. In imaging optics, we have demonstrated EUVL's feasibility as a lithographic candidate by establishing a design employing two-aspherical mirror optics, processing the aspherical mirrors with a multilayer coating, devising an assembly technology for imaging optics, and realizing an illumination system for large exposure area. This result showing the possibility of large-area exposure constitutes an epoch that strongly promotes the practical application of EUVL. Also, at-wavelength metrology in the EUV wavelength region, such as mask inspection based on a Mirau interferometric microscope, or thin film analysis based on a soft X-ray ellipsometer has contributed greatly to the practical application of EUVL.