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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. We present an alternative hypothesis explaining both tree-grass coexistence and woody plant encroachment in arid savannas. We propose that woody plant encroachment is part of a cyclical succession between open savanna and woody dominance and is driven by two factors: rainfall that is highly variable in space and time, and inter-tree competition. In this case, savanna landscapes are composed of many patches (a few hectares in size) in different states of transition between grassy and woody dominance, i.e. we hypothesize that arid savannas are patch-dynamic systems. We summarize patterns of tree distribution observed in an arid savanna in Namibia and show that these patterns are in agreement with the patch-dynamic savanna hypothesis. We discuss the applicability of this hypothesis to fire-dominated savannas, in which rainfall variability is low and fire drives spatial heterogeneity. We conclude that field studies are more likely to contribute to a general understanding of tree-grass coexistence and woody plant encroachment if they consider both primary (rain and nutrients) and secondary (fire and grazing) determinants of patch properties across different savannas.