Male butterflies in the hyperdiverse tribe Eumaeini possess an unusually complex and diverse repertoire of secondary sexual characteristics involved in pheromone production and dissemination. Maintaining multiple sexually selected traits is likely to be metabolically costly, potentially resulting in trade-offs in the evolution of male signals. However, a phylogenetic framework to test hypotheses regarding the evolution and maintenance of male sexual traits in Eumaeini has been lacking. Here, we infer a comprehensive, time-calibrated phylogeny from 379 loci for 187 species representing 91% of the 87 described genera. Eumaeini is a monophyletic group that originated in the late Oligocene and underwent rapid radiation in the Neotropics. We examined specimens of 818 of the 1096 described species (75%) and found that secondary sexual traits are present in males of 91% of the surveyed species. Scent pads and scent patches on the wings and brush organs associated with the genitalia were probably present in the common ancestor of Eumaeini and are widespread throughout the tribe. Brush organs and scent pads are negatively correlated across the phylogeny, exhibiting a trade-off in which lineages with brush organs are unlikely to regain scent pads and vice versa. In contrast, scent patches seem to facilitate the evolution of scent pads, although they are readily lost once scent pads have evolved. Our results illustrate the complex interplay between natural and sexual selection in the origin and maintenance of multiple male secondary sexual characteristics and highlight the potential role of sexual selection spurring diversification in this lineage.