In its chapter "Modeling," the International Technology Roadmap for Semiconductor 2005 edition stipulates the need for "Multi-generation lithography system models." Most lithographers would share this opinion that even if the equipment needs constant refurbishing, the software should survive at least a couple of technology generations. Fortunately, the table in which the statement appeared in the ITRS roadmap was accurately entitled "difficult challenges." This article will shed some light on the process of progressive modeling while making clear that, in all likelihood, formidable challenges will remain. The very core of simulation is a physical / chemical model of the real world. Lithographers need a sound model for the next technology node, not a short-sighted one, despite the fact that this is very difficult to achieve. This paper will use the parable of the ichthyologist as a starting point for the problem. It will translate the parable into the "deep waters" of lithography, showcasing lithography simulation as it has evolved over the years. Finally, it will present a small, yet decisive, recent step toward predictive lithography simulation. This example will include an improvement in the model for the post-exposure bake of chemically amplified resists, as well as a non-comprehensive list of foreseeable challenges.