As first generation extreme ultraviolet lithography (EUVL) systems go into the hands of lithographers, the obstacles to full production are reducing in number and scope. Chief among these remaining obstacles, however, is the source power. Although source manufacturers have made remarkable recent progress, power levels are still far below what is needed for production tools. This makes the importance of an efficient illumination system even more so as Moore's law pushes the industry to resolutions requiring EUVL. This paper describes some of the special issues for EUVL illumination systems, discusses several modeling tools appropriate to EUVL illumination systems, with examples based on fly's eye and debris mitigation systems found in the literature.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.