For tropical forests to survive anthropogenic climate change, the trees that comprise them will need to tolerate the newly emerging conditions through adaptation or acclimation, or they can avoid climate change through range shifts and “species migrations”. In this review, we show that the rapid pace and extreme severity of modern climate change makes it extremely unlikely that tropical tree species can adapt (with some possible exceptions). We also show that while many tropical tree species are shifting their distributions to higher, cooler elevations, the rate of these migrations are mostly insufficient to offset ongoing changes in temperatures, especially in lowland tropical rainforests where thermal gradients are shallow or nonexistent. We argue that the best hope for tropical tree species to avoid becoming “committed to extinction” is acclimation. While several new methods are being developed to test for acclimation, we unfortunately still do not know if tropical tree species can acclimate or what factors may prevent or facilitate acclimation. Until these questions are answered, our ability to predict the fate of tropical species and tropical forests – and the many services that they provide to humanity – remains critically impaired.