Elucidating the mechanism that maintains tree diversity in tropical rainforests is one of the compelling ecological challenges of our time. The longevity and inherent rarity of tropical tree species, combined with species losses due to anthropogenic change, provide additional stumbling blocks to resolving this issue. However, conceptual theory combined with sophisticated statistical techniques provide a way to overcome these issues. Despite differences in ecological dynamics and evolutionary trajectories, tree species are subject to a common set of ecophysiological constraints. These constraints provide a common denominator for elucidating the mechanisms by which large numbers of seemingly different species coexist within a forest. Plant ecophysiology provides the advantage of common metrics, such as plant functional traits, which in turn provide reliable proxies for characterizing the set of ecophysiological strategies adopted for rainforest tree species. Such trait-based approaches have proved essential in advancing our understanding of species coexistence in many different types of plant communities. Here I work to elucidate the coexistence mechanisms underlying the rich diversity of tree species in the Amazon rainforest. I develop a framework centered on an ecophysiological constraint --- allocation trade-offs, which I argue, is foundational to tree species coexistence. The argument is as follows. Individuals are ultimately limited by the energy they extract from essential limiting resources. Resource limitation means unequal energy allocation to traits underlying survival, growth and reproduction: higher survival comes at the cost of reduced growth or lower reproduction. Within a given environment, species-specific differences in allocation trade-offs can generate only fitness differences and competitive exclusion (the R* rule). However, in variable environments inter-specific differences in allocation trade-offs can lead to species-specific responses to environmental variation. Commonly termed performance trade-offs, these species-specific differences can allow species to limit themselves more than they do others, leading to niche differences and stable, long-term coexistence. I use this conceptual framework in my dissertation to elucidate tree species coexistence mechanisms in one of the most complex biological systems on the planet: the hyperdiverse forests of the Central Amazon. My work shows how allocation trade-offs that occur at the individual level can explain phenotypic trait diversity at different organizational levels, including nutrients within leaves (Ch.1), leaves within crowns (Ch.2), whole-plant allometries (Ch.3), and tree life-history (Ch.4). I use statistical models based on the Hierarchical Bayesian approach to connect species’ trait data with their spatial distributions for over a thousand different species. I make the following key findings: 1) leaf nutrient allocation trade-offs arising from interactions with root symbionts can lead to diverging habitat specialization among tree species (Ch.1); 2) an imperfect leaf size-number trade-off can explain interspecific variation in shade tolerance in saplings (Ch.2); 3) a relaxed trade-off between height-gain and crown expansion in saplings allows for a decoupling between sapling and adult niches (Ch.3); and 4) the growth-reproduction trade-off underlies vertical niche segregation in adult trees (Ch.4). These four core results reinforce the importance of allocation trade-offs as the fundamental driver of niche divergence and coexistence of forest tree species. Furthermore, because the four allocation trade-offs studied here are only a small sample of the multitude of trade-offs that limit plant performance, combining only a handful of trade-offs could potentially explain a great deal of the hyperdiversity of trees seen in these Amazonian forests.