Forest and savanna biomes dominate the tropics, yet factors controlling their distribution remain poorly understood. Climate is clearly important, but extensive savannas in some high rainfall areas suggest a decoupling of climate and vegetation. In some situations edaphic factors are important, with forest often associated with high nutrient availability. Fire also plays a key role in limiting forest, with fire exclusion often causing a switch from savanna to forest. These observations can be captured by a broad conceptual model with two components: (1) forest and savanna are alternative stable states, maintained by tree cover-fire feedbacks, (2) the interaction between tree growth rates and fire frequency limits forest development; any factor that increases growth (e.g. elevated availability of water, nutrients, CO2), or decreases fire frequency, will favour canopy closure. This model is consistent with the range of environmental variables correlated with forest distribution, and with the current trend of forest expansion, likely driven by increasing CO2 concentrations. Resolving the drivers of forest and savanna distribution has moved beyond simple correlative studies that are unlikely to establish ultimate causation. Experiments using Dynamic Global Vegetation Models, parameterised with measurements from each continent, provide an important tool for understanding the controls of these systems.