Considerable effort has been devoted over the last decade to the development of extreme ultraviolet (EUV) light sources for nanolithography. The 13.5 nm wavelength was imposed by industrial standards due to the availability of high-reflectivity Mo/Si multilayer mirrors so that a resolution of 32 nm can be attained. Xenon and tin are considered to be the best candidates for EUV light sources. In this review we first briefly introduce the concepts and principle of EUV lithography, and then discuss recent progress in both experimental and theoretical research on laser produced and gas discharge produced plasma light sources, with emphasis on the emission and absorption properties of xenon and tin plasmas. Theoretical studies show that statistical physical models are not yet able to predict the exact absorption and emission spectra of EUV plasmas. It is imperative that a detailed energy level model be developed to obtain accurate optical parameters to guide experimental design and to improve EUV conversion efficiency.