We take a case-based approach to teach contemporary mathematical modeling techniques. The course is appropriate for advanced undergraduates and beginning graduate students. Lectures provide biological background and describe the development of both classical mathematical models and more recent representations of biological processes. The course will be useful for students who plan to use experimental techniques as their approach in the laboratory and employ computational modeling as a tool to draw deeper understanding of experiments. The course should also be valuable as an introductory overview for students planning to conduct original research in modeling biological systems.