Estimates of extinction risk for Amazonian plant and animal species are rare, and not often incorporated into land-use policy and conservation planning. Here we overlay spatial distribution models with historical and projected deforestation to show that at least 40% and up to 64% of all Amazonian tree species are likely to qualify as globally threatened under IUCN Red List criteria. If confirmed, these results would increase the number of threatened plant species on Earth by 22%. We further show that the trends observed in Amazonia apply to trees throughout the tropics, and predict that most of the world's >40,000 tropical tree species currently qualify as globally threatened. A gap analysis suggests that existing Amazonian protected areas and indigenous territories will protect viable populations of most threatened species if those areas suffer no further degradation, highlighting the key roles that protected areas, indigenous peoples, and improved governance can play in preventing large-scale extinctions in the tropics in this century.