Global warming is forcing many species to shift their distributions upward, causing consequent changes in the compositions of species that occur at specific locations. This prediction remains largely untested for tropical trees. Here we show, using a database of nearly 200 Andean forest plot inventories spread across more than 33.5° latitude (from 26.8° S to 7.1° N) and 3,000-m elevation (from 360 to 3,360 m above sea level), that tropical and subtropical tree communities are experiencing directional shifts in composition towards having greater relative abundances of species from lower, warmer elevations. Although this phenomenon of 'thermophilization' is widespread throughout the Andes, the rates of compositional change are not uniform across elevations. The observed heterogeneity in thermophilization rates is probably because of different warming rates and/or the presence of specialized tree communities at ecotones (that is, at the transitions between distinct habitats, such as at the timberline or at the base of the cloud forest). Understanding the factors that determine the directions and rates of compositional changes will enable us to better predict, and potentially mitigate, the effects of climate change on tropical forests.