Spontaneous activity of specific regions (e.g., the Sinoatrial node, SAN) is essential for the normal activation sequence of the heart and also serve as a primary means of modulating cardiac rate by sympathetic tone and circulating catecholamines. The mechanisms of how a small SAN region can electrically drive a much larger atrium, or how a small ectopic focus can drive surrounding ventricular or atrial tissue are complex, and involve the membrane properties and electrical coupling within the SAN or focus region as well as the membrane properties, coupling conductance magnitudes and also regional distribution within the surrounding tissue. We review here studies over the past few decades in which mathematical models and experimental studies have been used to determine some of the design principles of successful propagation from a pacemaking focus. These principles can be briefly summarized as (1) central relative uncoupling to protect the spontaneously firing cells from too much electrotonic inhibition, (2) a transitional region in which the cell type and electrical coupling change from the central SAN region to the peripheral atrial region, and (3) a distributed anisotropy to facilitate focal activity.