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 () ideas of how successful philopatric or dispersing individuals are at gaining mates or the resources required to attract them. Theory, however, has developed surprisingly independently of these ideas: models typically track how immigration and emigration change relatedness patterns and alter competition for limiting resources. The limiting resources are often considered sexually distinct, with breeding sites and fertilizable 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. Here, an important understudied factor is the extent to which movement is interpretable as an extension of mate-searching (e.g. are matings possible en route or do they only happen after settling in new habitat - or can females perhaps move with stored sperm). We also point out other new directions for bridging the gap between empirical and theoretical studies: there is a need to build Greenwood's influential yet verbal explanation into formal models, which also includes the possibility that an individual benefits from mobility as it leads to fitness gains in more than one final breeding location (a possibility not present in models with a very rigid deme structure). The order of life-cycle events is likewise important, as this impacts whether a departing individual leaves behind important resources for its female or male kin, or perhaps both, in the case of partially overlapping resource use.
