When aggression is conceptualised in terms of a cost-benefit ratio, sex differences are best understood by a consideration of female costs as well as male benefits. Benefits must be extremely high to outweigh the greater costs borne by females, and circumstances where this occurs are discussed. Achievement of dominance is not such a circumstance and evidence bearing upon women's egalitarian relationships is reviewed. Attempts to explain sex differences in terms of sexual dimorphism, sex-of-target effects, social control, and socialisation are found to be inadequate. The suggestion that the stigmatisation of female aggreession arises not from patriarchal imposition but from statistical rarity (resulting from evolutionary pressures) is given serious consideration. Two hypotheses (“internal read-out” versus social/epidemiological representations) are described to explain the relationship between sex differences in behaviour and corresponding lay explanations.