In the last 35 years modeling of projection printing has undergone many paradigm shifts in physical models, computational engines, algorithms and opportunities. The trigger event for the first quantitative positive resist Dill model was the development and application of automated thin-film measurement equipment. The use of partial coherence which helps imaging also complicates the understanding and necessitates the use of simulation to guide lithography practice. Simulation has also played an important role in discovery (intensity imbalance in phase-shifting masks), invention (self-interferometric mask monitors) and creation of analysis techniques (first-cut accurate fast-CAD). The current challenges and growth areas for simulation include calibration, synergy with metrology, electronic self-testing and linking circuit design and fabrication.