EUV lithography is the most promising candidate for the replication of patterns for the 45-nm technology node and below. There are many issues in EUV lithography currently under intensive investigation. They concern (1) a high-power light source, (2) aspherical optics, (3) the exposure system, (4) multilayer coatings, (5) defect-free masks and (6) resist processes. This paper reports on recent research in all these areas except the high power light source. The required output power of the light source is discussed based on a detailed analysis of throughput. However, there are many parameters related to throughput. In this regard, it should be noted that not only a light source with a higher output power but also more sensitive resists and more reflective multilayer mirrors are indispensable if EUV lithography is to become a practical tool.