Understanding the capacity of forests to adapt to climate change is of pivotal importance for conservation science, yet this is still widely unknown. This knowledge gap is particularly acute in high-biodiversity tropical forests. Here, we examined how tropical forests of the Americas have shifted community trait composition in recent decades as a response to changes in climate. Based on historical trait-climate relationships, we found that, overall, the studied functional traits show shifts of less than 8% of what would be expected given the observed changes in climate. However, the recruit assemblage shows shifts of 21% relative to climate change expectation. The most diverse forests on Earth are changing in functional trait composition but at a rate that is fundamentally insufficient to track climate change.