Sexual differences are often dramatic and widespread across taxa. Their extravagance and ubiquity can be puzzling because the common underlying genome of males and females is expected to impede rather than foster phenotypic divergence. Widespread dimorphism, despite a shared genome, may be more readily explained by considering the multivariate, rather than univariate, framework governing the evolution of sexual dimorphism. In the univariate formulation, differences in genetic variances and a low intersexual genetic correlation () can facilitate the evolution of sexual dimorphism. However, studies that have analysed sex-specific differences in heritabilities or genetic variances do not always find significant differences. Furthermore, many of the reported estimates of are very high and positive. When monomorphic heritabilities and a high are present together, the evolution of sexual dimorphism on a trait-by-trait basis is severely constrained. By contrast, the multivariate formulation has greater generality and more flexibility. Although the number of multivariate sexual dimorphism studies is low, almost all support sex-specific differences in the G (variance-covariance) matrix; G matrices can differ with respect to size and/or orientation, affecting the response to selection differently between the sexes. Second, whereas positive values of the univariate quantity only hinder positive changes in sexual dimorphism, positive covariances in the intersexual covariance B matrix can either help or hinder. Similarly, the handful of studies reporting B matrices indicate that it is often asymmetric, so that B can affect the evolution of single traits differently between the sexes. Multivariate approaches typically demonstrate that genetic covariances among traits can strongly constrain trait evolution when compared with univariate approaches. By contrast, in the evolution of sexual dimorphism, a multivariate view potentially reveals more opportunities for sexual dimorphism to evolve by considering the effect sex-specific selection has on sex-specific G matrices and an asymmetric B matrix.