1. Endothelium-derived hyperpolarization (EDH) has been reported in many vessels and an extensive literature suggests that a novel, non-nitric oxide and non-prostanoid, endothelium-derived factor(s) may be synthesized in endothelial cells. 2. The endothelium-dependent hyperpolarizing factor, or EDHF, is synthesized by the putative EDHF synthase and mediates its cellular effects by either, directly or indirectly, opening K channels on vascular smooth muscle cells or, via hyperpolarization of the endothelial cell, by facilitating electrical coupling between the endothelial and the vascular smooth muscle cell. 3. The question of the chemical identity of EDHF has received considerable attention; however, no consensus has been reached. Tissue and species heterogeneity exists that may imply there are multiple EDHF. Leading candidate molecules for EDHF include an arachidonic acid product, possibly an epoxygenase product, or an endogenous cannabinoid, or simply an increase in extracellular K+. 4. An increasing body of evidence suggests that EDH, notably in the resistance vasculature, may be mediated via electrical coupling through myoendothelial gap junctions and the existence of electrical coupling may negate the need to hypothesize the existence of a true endothelium-derived chemical mediator. 5. In this paper we review the evidence that supports and refutes the existence of a novel EDHF versus a hyperpolarization event mediated solely by myoendothelial gap junctions.