These lecture notes are intended to describe the topic of my plenary talk at the European Modeling and Simulation Symposium, in Barcelona, October, 2006. When graciously presented with the opportunity to give this talk, my thoughts went naturally to questions that I've found fascinating all of my professional life : what are the relationships between the expressiveness one uses in modeling to one's ability to efficiently extract useful behavioral information, and the validity of the simulations so produced? I'd love to be able to talk about general answers to these questions, but I've not discovered them. What I can do is describe some of the issues and tradeoffs I've personally encountered, and the contexts in which I've encountered them. I can hope that those versed in other application domains gain some insight into their problems, based on insights I've had in mine.