1. This paper reviews evidence for five functional explanations of the evolution of antlers in male cervids: that they are used as weapons in fights; that they allow individuals to defend themselves against predators; that they act as heat radiators during their period of growth; that they advertise an individual's fighting ability and allow males to assess each other without fighting; and that they increase the chances that a male will be selected as a mate by females. 2. There is extensive evidence that antlers are used in fights between competing males. Contrary to some suggestions in the literature, fights are regular during the breeding season and can be damaging. In species where fighting behaviour has been studied in detail, antlers have proved to be effective weapons of defence and offense, and there is no systematic evidence to support the suggestion that antler-less males (hummels) are more successful in competition for females than antlered stags. 3. Though male deer sometimes use their antlers in defence against predators, the absence of antlers in females of most species suggests that this is not their principal function. Nor does it seem likely that antlers evolved as heat-regulating mechanisms - in some species, they are grown during the winter months and there is no tendency for them to be larger in tropical species than in temperate ones. 4. Despite many suggestions, there is no conclusive evidence that males assess each other by their relative antler size and most measures of antler size and shape are not closely correlated with dominance or fighting ability. Nor is there firm evidence that females selectively mate with large-antlered males. 5. The absence of unequivocal support for the importance of antlers in defence against predators, in heat regulation, in assessment between rivals and in attracting mates leaves open the possibility that, despite their bizarre appearance, antlers evolved as weapons and are retained by selection because of their function in intra-specific combat.