The Amazon rainforest plays a crucial role in the climate system, helping to drive atmospheric circulations in the tropics by absorbing energy and recycling about half of the rainfall that falls on it. This region (Amazonia) is also estimated to contain about one-tenth of the total carbon stored in land ecosystems, and to account for one-tenth of global, net primary productivity. The resilience of the forest to the combined pressures of deforestation and global warming is therefore of great concern, especially as some general circulation models (GCMs) predict a severe drying of Amazonia in the twenty-first century. Here we analyse these climate projections with reference to the 2005 drought in western Amazonia, which was associated with unusually warm North Atlantic sea surface temperatures (SSTs). We show that reduction of dry-season (July-October) rainfall in western Amazonia correlates well with an index of the north-south SST gradient across the equatorial Atlantic (the 'Atlantic N-S gradient'). Our climate model is unusual among current GCMs in that it is able to reproduce this relationship and also the observed twentieth-century multidecadal variability in the Atlantic N-S gradient, provided that the effects of aerosols are included in the model. Simulations for the twenty-first century using the same model show a strong tendency for the SST conditions associated with the 2005 drought to become much more common, owing to continuing reductions in reflective aerosol pollution in the Northern Hemisphere.