Three models--the war of attrition, the size game and the badges of dominance game--are described, in which natural selection can maintain genetic variability for aggression. The models differ in whether or not the traits that settle contests are costly in contexts other than fighting, and also in whether signals are used. It is concluded that contests will be settled by non-costly traits only if the value of the contested resource is small relative to the cost of fighting, and that 'honest' signalling of aggressiveness is stable only if individuals giving signals that are inconsistent with their behaviour suffer costs. The literature on 'badges of dominance' in birds is reviewed. New data on great tits, greenfinches and corn buntings show that there is plumage variability within age and sex that sometimes serves to settle contests, and that, in the first two species but not the third, the badges are uncorrelated with size, and settle contests only over trivial resources.