The coexistence of woody and grassy plants in savannas has often been attributed to a rooting-niche separation (two-layer hypothesis). Water was assumed to be the limiting resource for both growth forms and grasses were assumed to extract water from the upper soil layer and trees and bushes from the lower layers. Woody plant encroachment (i.e. an increase in density of woody plants often unpalatable to domestic livestock) is a serious problem in many savannas and is believed to be the result of overgrazing in 'two-layer systems'. Recent research has questioned the universality of both the two-layer hypothesis and the hypothesis that overgrazing is the cause of woody plant encroachment. Keywords: fire, grazing, honeycomb rippling model, inter-tree competition, spatio-temporal rainfall variation, tree-grass coexistence.