The Electrical Thresholds of Ventricular Myocardium. According to the basic principles of electrophysiology, an action potential cannot propagate three‐dimensionally if its front is too sharply curved. The critical radius of curvature is estimated for ventricular myocardium as 1/3 mm and checked against experimental determinations of the pacing threshold. An implication of the agreement found is that pacemaker electrodes can be improved by optimizing their tip curvatures. The same basic principles imply that there should exist a vortex‐like action potential, which has in fact heen found in both two‐ and three‐dimensional settings. It rotates in 120 msec and has a 2/3‐cm diameter. This diameter can he used to derive the electrical threshold for fibrillation in normal ventricular myocardium: ahout 16 mA, depending on electrode geometry. This compares favorably with ohservations. As theory suggests, the ratio of this threshold to the pacing threshold seems independent of pulse duration and depends on electrode geometry: the minimum ratio is about five for large electrodes. Electrical defihrillation in normal myocardium should require local potential gradients of about 6 V/cm or current densities near 20 mA/cm2, roughly as observed, but much more uniform deHhrillating fields are needed to achieve this theoretical minimum throughout the myocardium. It is suggested that in normal myocardium, the transition from monomorphic tachycardia or ventricular flutter to fibrillation in some cases may be a consequence of the three‐dimensional geometry of vortex‐like action potentials; the transition should take a long time in two‐dimensional preparations unless they are pervaded hy discontinuities or other nonuniformities. (J Cardiovasc Electrophysiol, Vol. 1, pp. 393–410, October 1990)