The intercalated discs that connect cardiomyocytes control cell-to-cell adhesion and communication. Several macromolecular structures (desmosomes, fascia adherens junctions, gap junctions, and sodium-channel complexes) coexist in, and confer their mechanical and electrical properties to, the intercalated disc. Traditionally, each structure was assumed to have a unique function in the intercalated disc. However, growing evidence suggests that these complexes act together in intercellular communication and adhesion, forming a single structural and functional entity — the connexome. This nascent idea has provided conceptual support for the overlapping of two diseases based on disturbance of the intercalated disc — arrhythmogenic cardiomyopathy (ACM) and Brugada syndrome (BrS). In this Perspectives article, we present the latest findings about the functions of, and interactions between, the structures of the intercalated disc that support the concept of the connexome. We also summarize the genetic, molecular, and pathophysiological mechanisms underlying ACM and BrS, focusing on the overlap between these diseases.