Competition over mates takes many forms and has far-reaching consequences for many organisms. Recent work suggests that relative reproductive rates of males and females, sperm competition and quality variation among mates affect the strength of sexual selection. Song, other display, body size, visual ornaments and material resource offerings are often sexually selected. There is much empirical evidence of mate choice, and its evolution is clarified by mathematical models. Recent advances in theory also consider costs of choice, effects of deleterious mutations, fast and slow evolution of preferences and preferred traits, and simultaneous preferences for several traits. Contests over mates are important; so is sperm competition, scrambles, endurance rivalry, and coercion. The latter mechanisms have received less attention than mate choice. Sexual selection may explain puzzling aspects of plant pollination biology.