For EUV lithography the generation of clean and efficient light source and the high-power laser technology are key issues. Theoretical understanding with modeling and simulation of laser-produced EUV source based on detailed experimental database gives us the prediction of optimal plasma conditions and their suitable laser conditions for different target materials (tin, xenon and lithium). With keeping etendue limit the optimal plasma size is determined by an appropriate optical depth which can be controlled by the combination of laser wavelength and pulse width. The most promising candidate is tin (Sn) plasma heated by Nd:YAG laser with a pulse width of a few ns. Therefore the generation technology of clean Sn plasma is a current important subject to be resolved for practical use. For this purpose we have examined the feasibility of laser-driven rocket-like injection of extremely mass-limited Sn or SnO2 (punched-out target) with a speed exceeding 100m/s. Such a mass-limited low-density target is most preferable for substantial reduction of ion energy compared with usual bulk target. For high average power EUV generation we are developing a laser system which is CW laser diode pumped Nd:YAG ceramic laser (master oscillator and power amplifier system) operating at 5-10 kHz repetition rate. The design of practical laser for EUV source is being carried out based on the recent performance of >1 kW output power.