The membranes of glial cells are highly selectively permeable to potassium. The implications of this and the possible reasons for it are discussed. Glial cells may contribute to buffering the extracellular K+ concentration of brain tissue through several mechanisms. However, the only one that benefits from the K+ selective permeability is the so-called 'spatial' buffer mechanism, which acts more effectively than extracellular diffusion in many situations to speed the dispersal of local accumulations of potassium. The role of glial cells in buffering the extracellular K+ concentration may help to prevent the occurrence of a phenomenon called Leão's spreading depression (SD). A K+-induced K+ efflux from neurones, occurring when the EC K+ concentration rises above critical levels, is probably crucial in causing SD. The models that have been proposed to describe this process are discussed and related. Spreading depression is not known definitely to occur in man. It seems probable, however, that it occurs during attacks of 'classical' migraine, associated with neurological symptoms. These neurological symptoms have often been attributed to vasoconstriction rather than to SD since certain vasodilators can relieve the symptoms. Experiments with SD in anaesthetized rats show that at least one of these vasodilator interventions (administration of a CO2/O2 mixture) stops also the propagation of a wave of SD. This strengthens the evidence for a possible relationship between migraine and SD. The involvement of SD in migraine probably deserves more critical attention than has hitherto been devoted to it.