Bright colours, enlarged fins, feather plumes, song, horns, antlers and tusks are often highly sex dimorphic. Why have males in many species of animals evolved more conspicuous ornaments, signals and weapons than females? How can such traits evolve although they may reduce male survival? Such questions prompted Darwin's perhaps most scientifically controversial idea - the theory of sexual selection. This still challenges researchers today as they try to understand how competition for mates can favour the variety of sex-dimorphic traits. Reviewing theoretical and empirical work in this field, Malte Andersson provides a major up-to-date summary of sexual selection. The author describes the theory and its recent development; examines models, methods and empirical tests; and identifies many unsolved problems. Among the topics discussed are the selection and evolution of mating preferences; relations between sexual selection and speciation; constraints on sexual selection; and sex differences in signals, body size and weapons.