The term endothelium-derived hyperpolarising factor (EDHF) was introduced in 1987 to describe the hypothetical factor responsible for myocyte hyperpolarisations not associated with nitric oxide (EDRF) or prostacyclin. Two broad categories of EDHF response exist. The classical EDHF pathway is blocked by apamin plus TRAM-34 but not by apamin plus iberiotoxin and is associated with endothelial cell hyperpolarisation. This follows an increase in intracellular [Ca²⁺] and the opening of endothelial SK_Ca and IK_Ca channels preferentially located in caveolae and in endothelial cell projections through the internal elastic lamina, respectively. In some vessels, endothelial hyperpolarisations are transmitted to myocytes through myoendothelial gap junctions without involving any EDHF. In others, the K⁺ that effluxes through SK_Ca activates myocytic and endothelial Ba²⁺-sensitive K_IR channels leading to myocyte hyperpolarisation. K⁺ effluxing through IK_Ca activates ouabain-sensitive Na⁺/K⁺-ATPases generating further myocyte hyperpolarisation. For the classical pathway, the hyperpolarising “factor” involved is the K⁺ that effluxes through endothelial K_Ca channels. During vessel contraction, K⁺ efflux through activated myocyte BK_Ca channels generates intravascular K⁺ clouds. These compromise activation of Na⁺/K⁺-ATPases and K_IR channels by endothelium-derived K⁺ and increase the importance of gap junctional electrical coupling in myocyte hyperpolarisations. The second category of EDHF pathway does not require endothelial hyperpolarisation. It involves the endothelial release of factors that include NO, HNO, H₂O₂ and vasoactive peptides as well as prostacyclin and epoxyeicosatrienoic acids. These hyperpolarise myocytes by opening various populations of myocyte potassium channels, but predominantly BK_Ca and/or K_ATP, which are sensitive to blockade by iberiotoxin or glibenclamide, respectively.