The extent of the savannah biome is expected to be profoundly altered by climatic change and increasing atmospheric CO 2 concentrations. Contrasting projections are given when using different modelling approaches to estimate future distributions. Furthermore, biogeographic variation within savannahs in plant function and structure is expected to lead to divergent responses to global change. Hence the use of a single model with a single savannah tree type will likely lead to biased projections. Here we compare and contrast projections of South American, African and Australian savannah distributions from the physiologically based Thornley transport resistance statistical distribution model (TTR-SDM)—and three versions of a dynamic vegetation model (DVM) designed and parametrized separately for specific continents. We show that attempting to extrapolate any continent-specific model globally biases projections. By 2070, all DVMs generally project a decrease in the extent of savannahs at their boundary with forests, whereas the TTR-SDM projects a decrease in savannahs at their boundary with aridlands and grasslands. This difference is driven by forest and woodland expansion in response to rising atmospheric CO 2 concentrations in DVMs, unaccounted for by the TTR-SDM. We suggest that the most suitable models of the savannah biome for future development are individual-based dynamic vegetation models designed for specific biogeographic regions. This article is part of the themed issue ‘Tropical grassy biomes: linking ecology, human use and conservation’.