Three major hypotheses, based upon mechanisms of sexual selection, intersexual food competition and reproductive role division, have been advanced to explain the evolution of sexual dimorphism in body size and morphology of animals. Genetic models suggest that all of the hypotheses are plausible, and empirical studies demonstrate that each of the three mechanisms operates in natural populations. However, problems arise in testing hypotheses for the evolution of sexual dimorphism: more than one mechanism may be operating simultaneously, and the demonstrated occurrence of a mechanism does not indicate that it actually results in selection for dimorphism. A recent statistical technique offers a solution to these problems and provides a promising new approach to the study of sexual dimorphism, in which researchers can assess the relative importance of each mechanism in present-day selection for sexual dimorphism within a species. Copyright © 1989. Published by Elsevier Ltd.