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Dispersal, the tendency for organisms to reproduce away from their parents, influences many evolutionary and ecological processes, from speciation and extinction events, to the coexistence of genotypes within species or biological invasions. Understanding how dispersal evolves is crucial to predict how global changes might affect species persistence and geographical distribution. The factors driving the evolution of dispersal have been well characterized from a theoretical standpoint, and predictions have been made about their respective influence on, for example, dispersal polymorphism or the emergence of dispersal syndromes. However, the experimental tests of some theories remain scarce partly because a synthetic view of theoretical advances is still lacking. Here, we review the different ingredients of models of dispersal evolution, from selective pressures and types of predictions, through mathematical …