Introduction: Tropical forests represent key terrestrial ecosystems for carbon stocks and biodiversity. The dynamics of carbon storage in forests are primarily driven by tree performance in terms of mortality and growth. But climate change is altering tree performance, with important consequences for carbon cycle, climate regulation and biodiversity. Yet, we are still lacking accurate predictions of the response of tropical forest in terms of their composition, dynamics, and functions to altered climate. While demographic approaches have traditionally focused on how individual performance vary with ontogeny or size, trait-based approaches have focused on how morphological or physiological properties of individuals (traits) change with abiotic and biotic factors and links to performance. Though the link between traits and performance influences population dynamics and subsequent community structure and ecosystem functions, we still understand little about the drivers shaping the trait-performance relationship, and in the context of climate change, about how species traits may mediate differential growth sensitivities to average climate conditions or climate anomalies. Methods: Here, we use a set of complementary Bayesian multilevel models to understand the effects of average climate conditions and climate anomalies on decades of multi-annual tree growth data encompassing multiple environmental gradients distributed across the tropical continents. We use morphological, chemical and physiological functional traits of over 700 tropical tree species distributed across our plots to test whether interspecific differences in growth sensitivity to climate can be accounted for by species traits known to affect growth in certain environmental contexts. Results: We show that tropical tree growth responds negatively to increasing anomalies in temperature and atmospheric evaporative demand (VPD), but growth sensitivity to these and other climatic drivers vary widely across species. These interspecific differences in average growth rate and growth sensitivity are partly accounted for by functional traits related to acquisition resource strategies. We also highlight a range of trade-offs in species positive and negative responses to average climatic conditions and climate anomalies, suggesting eco-evolutionary constraints related to local climatic variations and species biogeography and niche. Implications: Our work shows that both average climate conditions and climate anomalies shape tree growth in tropical forests across continents, and that species traits can help to understand the mechanisms underlying the variability of demographic responses to climate change. We also show that considering region-specific growth responses to climate is important for accurate predictions. This approach offers a promising way forward to forecast tropical forest dynamics under different climate trajectories.