This review article summarizes theoretical insights into the principles and mechanisms associated with reentrant activity in cardiac tissue. A mathematical ring model is used in computer simulations to investigate, at the cellular level, mechanistic aspects of initiation, perpetuation, and termination of reentry. Taking advantage of the ability to compute membrane processes in this model, we relate dynamic properties of the reentrant action potential (e.g., beat-to-beat alternans) to the underlying kinetics of membrane ionic channels. Effects on reentry of inhomogeneities in refractoriness, excitability, cellular coupling at gap junctions, and fiber cross-section are also studied.