In the field of cardiac electrophysiology, modeling has played a central role for many decades. However, even though the effort is well-established, it has recently seen a rapid and sustained evolution in the complexity and predictive power of the models being created. In particular, new approaches to modeling have allowed the tracking of parallel and interconnected processes that span from the nanometers and femtoseconds that determine ion channel gating to the centimeters and minutes needed to describe an arrhythmia. The connection between scales has brought unprecedented insight into cardiac arrhythmia mechanisms and drug therapies. This review focuses on the generation of these models from first principles, generation of detailed models to describe ion channel kinetics, algorithms to create and numerically solve kinetic models, and new approaches toward data gathering that parameterize these models. While we focus on application of these models for cardiac arrhythmia, these concepts are widely applicable to model the physiology and pathophysiology of any excitable cell.