Cardiac arrhythmias are an important cause of sudden cardiac death—a devastating manifestation of many underlying causes, such as heart failure and ischemic heart disease leading to ventricular tachyarrhythmias and ventricular fibrillation, and atrial fibrillation causing cerebral embolism. Cardiac electrical propagation is a main factor in the initiation and maintenance of cardiac arrhythmias. In the heart, gap junctions are the basic unit at the cellular level that host intercellular low-resistance channels for the diffusion of ions and small regulatory molecules. The dual voltage clamp technique enabled the direct measurement of electrical conductance between cells and recording of single gap junction channel openings. The rapid turnover of gap junction channels at the intercalated disk implicates a highly dynamic process of trafficking and internalization of gap junction connexons. Recently, non-canonical roles of gap junction proteins have been discovered in mitochondria function, cytoskeletal organization, trafficking, and cardiac rescue. At the tissue level, we explain the concepts of linear propagation and safety factor based on the model of linear cellular structure. Working myocardium is adequately represented as a discontinuous cellular network characterized by cellular anisotropy and connective tissue heterogeneity. Electrical propagation in discontinuous cellular networks reflects an interplay of three main factors: cell-to-cell electrical coupling, flow of electrical charge through the ion channels, and the microscopic tissue structure. This review provides a state-of-the-art update of the cardiac gap junction channels and their role in cardiac electrical impulse propagation and highlights a combined approach of genetics, cell biology, and physics in modern cardiac electrophysiology.