Connexins (Cxs) are integral membrane proteins that form high-conductance plasma membrane channels, allowing communication from cell to cell (via gap junctions) and from cells to the extracellular environment (via hemichannels). Initially described for their role in joining excitable cells (nerve and muscle), gap junctions (GJs) are found between virtually all cells in solid tissues and are essential for functional coordination by enabling the direct transfer of small signalling molecules, metabolites, ions, and electrical signals from cell to cell. Several studies have revealed diverse channel-independent functions of Cxs, which include the control of cell growth and tumourigenicity. Connexin43 (Cx43) is the most widespread Cx in the human body. The myriad roles of Cx43 and its implication in the development of disorders such as cancer, inflammation, osteoarthritis and Alzheimer's disease have given rise to many novel questions. Several RNA- and DNA-binding motifs were predicted in the Cx43 and Cx26 sequences using different computational methods. This review provides insights into new, ground-breaking functions of Cxs, highlighting important areas for future work such as transfer of genetic information through extracellular vesicles. We discuss the implication of potential RNA- and DNA-binding domains in the Cx43 and Cx26 sequences in the cellular communication and control of signalling pathways.