Aim: An emerging framework for tropical ecosystems states that fire activity is either "fuel build‐up limited" or "fuel moisture limited", that is, as you move up along rainfall gradients, the major control on fire occurrence switches from being the amount of fuel, to the moisture content of the fuel. Here we used remotely sensed datasets to assess whether interannual variability of burned area is better explained by annual rainfall totals driving fuel build‐up, or by dry season rainfall driving fuel moisture. Location: Pantropical savannas and grasslands. Time period: 2002–2016. Methods: We explored the response of annual burned area to interannual variability in rainfall. We compared several linear models to understand how fuel moisture and fuel build‐up effect (accumulated rainfall during 6 and 24 months prior to the end of the burning season, respectively) determine the interannual variability of burned area and explore if tree cover, dry season duration and human activity modified these relationships. Results: Fuel and moisture controls on fire occurrence in tropical savannas varied across continents. Only 24% of South American savannas were fuel build‐up limited against 61% of Australian savannas and 47% of African savannas. On average, South America switched from fuel limited to moisture limited at 500 mm/year, Africa at 800 mm/year and Australia at 1,000 mm/year of mean annual rainfall. Main conclusions: In 42% of tropical savannas (accounting for 41% of current area burned) increased drought and higher temperatures will not increase fire, but there are savannas, particularly in South America, that are likely to become more flammable with increasing temperatures. These findings highlight that we cannot transfer knowledge of fire responses to global change across ecosystems/regions—local solutions to local fire management issues are required, and different tropical savanna regions may show contrasting responses to the same drivers of global change. [ABSTRACT FROM AUTHOR]