Optical lithography modeling began in the early 1970s and represented the first serious attempt to describe lithography not as an art, but as a science. Thirty years later, optical lithography continues to make dramatic advances that enable the profitable continuation of Moore's Law. Most if not all of these advances would not be possible without the use of lithography simulators. This article will review the history of lithography simulation, describing a few of the milestone events and important lithographic advances that simulation enabled. This historical review will end with a characterization of the current state of lithography modeling and its important applications in chip design, process development, and manufacturing today. Finally, a prediction of future advances in simulation capabilities will be made as well as how these advances will help to move the industry forward. (c) 2005 American Vacuum Society.