Advances of tabletop electron storage rings for generating a brilliant extreme ultraviolet (EUV) or soft x-ray beam are discussed. An electron storage ring called MIRRORCLE-20SX currently provides a stored beam current with an average of 3 A, a 1-minute lifetime, 15 ms radiation damping time, and a beam size of about . We generate EUV by a thin-film target placed in the electron orbit. Photons in the wavelength around 13.9 nm is generated by an Si thin film, and 4.3 nm by a diamond-like carbon (DLC) film placed in the circulating electron beam. It is known from previous experimental studies that the mechanism of EUV emission is a synchrotron Cherenkov radiation (SCR). The observed photon power is by the DLC film. We report that SCR is suitable for EUV lithography (EUVL) because the spectrum is monochromatic, the radiation angular spread is as narrow as , and the emitter size can be . An optimized EUV source for lithography based on the tabletop synchrotron is proposed.