Dispersal is ubiquitous throughout the tree of life: factors selecting for dispersal include kin competition, inbreeding avoidance and spatiotemporal variation in resources or habitat suitability. These factors differ in whether they promote male and female dispersal equally strongly, and often selection on dispersal of one sex depends on how much the other disperses. For example, for inbreeding avoidance it can be sufficient that one sex disperses away from the natal site. Attempts to understand sex-specific dispersal evolution have created a rich body of theoretical literature, which we review here. We highlight an interesting gap between empirical and theoretical literature. The former associates different patterns of sex-biased dispersal with mating systems, such as female-biased dispersal in monogamous birds and male-biased dispersal in polygynous mammals. The predominant explanation is traceable back to Greenwood's (1980) ideas of how successful philopatric or dispersing individuals are at gaining mates or resources required to attract them. Theory, however, has developed surprisingly independently of these ideas: predominant ideas in theoretical work track how immigration and emigration change relatedness patterns and alleviate competition for limiting resources, typically considered sexually distinct, with breeding sites and fertilisable females limiting reproductive success for females and males, respectively. We show that the link between mating system and sex-biased dispersal is far from resolved: there are studies showing that mating systems matter, but the oft-stated association between polygyny and male-biased dispersal is not a straightforward theoretical expectation... (full abstract in the PDF)