Ubiquitously expressed connexins are tetra-spanning transmembrane proteins that form intercellular gap junction channels or cell surface hemichannels. Connexins share similar topology but no sequence homology with mammalian pannexins and CALHM1 (calcium homeostasis modulator 1), which are also large-pore transmembrane channels. Of these three channel types, clinical evidence and gene sequence analysis to date have revealed that inherited human diseases are only associated with mutations in the connexin gene family. Connexin-linked diseases often present at birth or early in life and range from mild developmental abnormalities to severe organ failure such as hearing loss. Inherited connexin gene mutations can manifest as a disease by causing anomalies or defects in connexin oligomerization, folding, ability to pass quality control mechanisms or unexpected gain- or loss-of-function. This review provides examples of the way that various connexin gene mutations can cause disease via a wide range of molecular mechanisms. We also reflect on exciting strategies being explored in the connexin field and beyond with a view of translating their findings into potential connexin-disease therapeutics.