Consistent individual behavioural tendencies, termed "personalities", have been identified in a wide range of animals. Functional explanations for personality have been proposed, but as yet, very little consideration has been given to a possible role for sexual selection in maintaining differences in personality and its stability within individuals. We provide an overview of the available literature on the role of personality traits in intrasexual competition and mate choice in both human and non-human animals and integrate this into a framework for considering how sexual selection can generate and maintain personality. For this, we consider the evolution and maintenance of both main aspects of animal personality: inter-individual variation and intra-individual consistency.