The merging of hypotheses and techniques from physics, mathematics, biomedical engineering, cardiology, and computer science is helping to form increasingly more realistic computer models of the heart. These models complement experimental and clinical studies that seek to elucidate the mechanisms of arrhythmogenesis and improve pharmacological and electrical therapies. This paper reviews the current state of the art of computer models for investigating normal and abnormal conduction in cardiac muscle. A brief introduction to the mathematical foundations of continuous (monodomain and bidomain) and discrete tissue structure models and to ionic current based and FitzHugh-Nagumo membrane models is presented. The paper summarizes some of the recent contributions in validating tissue structure models, modeling unidirectional block and reentry in a 1-D loop, and applying generic spiral wave theory to cardiac arrhythmias.