Thirty years ago Rick Dill and his team at IBM published the first account of lithography simulation -the accurate description of semiconductor optical lithography by mathematical equations. Since then, lithography simulation has grown dramatically in importance in four important areas: as a research tool, as a development tool, as a manufacturing tool, and as a learning tool. In this paper, the history of lithography simulations is traced from its roots to today's indispensable tools for lithographic technology development. Along the way, an attempt will be made to define the true value of lithography simulation to the semiconductor industry.