• We aimed to identify the limits of savanna across Africa, Australia and South America. We based our investigation on the rich history of hypotheses previously examined: that the limits of savanna are variously determined by rainfall, rainfall seasonality, soil fertility and disturbance. • We categorized vegetation on all continents as 'savanna' (open habitats with a C(4) grass layer) or 'not-savanna' (closed habitats with no C(4) grass layer) and used a combination of statistical approaches to examine how the presence of savanna varied as a function of five environmental correlates. • The presence of savanna is constrained by effective rainfall and rainfall seasonality. Soil fertility is regionally important, although the direction of its effect changes relative to rainfall. We identified three continental divergences in the limits of savanna that could not be explained by environment. • Climate and soils do not have a deterministic effect on the distribution of savanna. Over the range of savanna, some proportion of the land is always 'not-savanna'. We reconciled previous contradictory views of savanna limits by developing a new conceptual framework for understanding these limits by categorizing environmental factors into whether they had a positive or negative effect on woody growth and the frequency of disturbance.