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Biologists have long sought to understand the processes underlying disparities in clade size across the tree of life and the extent to which such clade size differences can be attributed to the evolution of particular traits. The association of certain character states with species-rich clades suggests that trait evolution can lead to increased diversification, but such a pattern could also arise due other processes, such as directional trait evolution. Recent advances in phylogenetic comparative methods have provided new statistical approaches for distinguishing between these intertwined and potentially confounded macroevolutionary processes. Here, we review the historical development of methods for detecting state-dependent diversification and explore what new methods have revealed about classic examples of traits that affect diversification, including evolutionary dead ends, key innovations and geographic traits. Applications of these methods thus far collectively suggest that trait diversity commonly arises through the complex interplay between transition, speciation and extinction rates and that long hypothesized evolutionary dead ends and key innovations are instead often cases of directional trends in trait evolution. [ABSTRACT FROM AUTHOR]