Endothelium-derived hyperpolarizing factor (EDHF) is defined as the non-nitric oxide (NO) and non-prostacyclin (PGI2) substance that mediates endothelium-dependent hyperpolarization (EDH) of vascular smooth muscle cells (VSMC). Although both NO and PGI2 have been demonstrated to hyperpolarize VSMC by cGMP- and cAMP-dependent mechanisms, respectively, and in the case of NO by cGMP-independent mechanisms, a considerable body of evidence suggests that an additional cellular mechanism must exist that mediates EDH. Despite intensive investigation, there is no agreement as to the nature of the cellular processes that mediates the non-NO/PGI2 mediated hyperpolarization. Epoxyeicosatrienoic acids (EET), an endogenous anandamide, a small increase in the extracellular concentration of K+, and electronic coupling via myoendothelial cell gap junctions have all been hypothesized as contributors to EDH. An attractive hypothesis is that EDH is mediated via both chemical and electrical transmissions, however, the contribution from chemical mediators versus electrical transmission varies in a tissue- and species-dependent manner, suggesting vessel-specific specialization. If this hypothesis proves to be correct then the potential exists for the development of vessel and organ-selective vasodilators. Because endothelium-dependent vasodilatation is dysfunctional in disease states (i.e., atherosclerosis), selective vasodilators may prove to be important therapeutic agents.