Females frequently mate with multiple males in a single reproductive episode, which creates the potential for sperm competition, a potent selective force that shapes male reproductive anatomy across the animal kingdom. However, relationships between sperm competition and reproductive traits at the interspecific level are generally inconsistent across taxa, and some key taxonomic groups are understudied or remain to be assessed, which limits the potential for evaluating the consistency of selection. In this thesis, I take a comparative approach to examine how sperm competition influences the evolution of reproductive traits in the elasmobranch fishes (sharks and rays). In spite of the extraordinary variation in reproductive systems and structures in this group, prior to this thesis we knew very little about the selective processes that have shaped them. First, I show that in shark species where females are more likely to mate with multiple males, or mate with a greater number of males, males invest in larger testes relative to body mass. This validates the use of body-size corrected testes mass as a proxy for sperm competition risk and intensity. Secondly, I demonstrate that reproductive traits exhibit variable responses to the level of sperm competition (as measured by body size-corrected testes mass). The length of the sperm flagellum appears to be a target of selection in both sharks and rays, though flagellum length is positively associated with sperm competition risk in sharks, whereas in rays the relationship is negative. In contrast, the structural organisation of the testes is not influenced by sperm competition in sharks, although there is tentative evidence to suggest that males from species at higher sperm competition risk have a higher proportion of sperm-producing tissue in the testes in rays. Finally, in sharks, the length of the male genitalia and presence or absence of genital appendages (spines, hooks and claws) are not associated with sperm competition risk, and only evolutionary losses of spines were detected across shark phylogeny. Overall, these findings provide new insights into post-mating selective dynamics in an ancestral vertebrate lineage and contribute to a wider understanding of how sexual selection acts on reproductive traits across the vertebrate tree of life.