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Heart rhythm disorders represent a significant global health concern, affecting millions of people worldwide and serving as a risk factor for heart failure. Despite the prevalence of these arrhythmias, broadly effective treatments remain elusive. In this work, we present the cardiac conduction system as an excitable medium whose dynamics can be described with simple mathematical models. We show that the excitation of this system can become altered through well-timed stimuli which create persistent rotational activation patterns. We describe the hypothesized relationship between these patterns and the perpetuation of fibrillation, discussing the fragmenting state of multi-wavelet reentry as well as the theory of mother rotors. To distinguish between potential mechanisms, we present results using concepts of phase synchrony to characterize clinical recordings of fibrillation. Such analysis implies a level of spatiotemporal stability inconsistent with a mechanism exclusively comprised of chaotic multi-wavelet reentry. Moreover, we outline a technique to determine continuously updating vector flow fields which align with the direction of local conduction. We show that this methodology can be used to determine the source of rotational and focal excitation patterns in an automated fashion, providing a useful means to interpret otherwise complex spatiotemporal maps. Finally, we describe the spontaneous termination of fibrillation as a stochastic event, and construct a birth-death Master equation for the number of spiral tips n during the turbulent state of spiral-defect chaos. Within this framework, we can infer important statistical quantities related to fibrillation such as the mean number of spiral tips n, the quasi-stationary distribution Pqs, and the mean episode duration t. Our results imply that t scales exponentially with the area A. We derive this scaling law using a WKB approach, which yields an effective Hamiltonian describing tip density q = n=A and fluctuation momentum p. This stochastic approach can accurately predict t, even for systems in which a multitude of episodes cannot be simulated due to prohibitive computational cost.