Horses, asses, and zebras belong to a single genus, Equus, which emerged 4.0-4.5 Mya. Although the equine fossil record represents a textbook example of evolution, the succession of events that gave rise to the diversity of species existing today remains unclear. Here we present six genomes from each living species of asses and zebras. This completes the set of genomes available for all extant species in the genus, which was hitherto represented only by the horse and the domestic donkey. In addition, we used a museum specimen to characterize the genome of the quagga zebra, which was driven to extinction in the early 1900s. We scan the genomes for lineage-specific adaptations and identify 48 genes that have evolved under positive selection and are involved in olfaction, immune response, development, locomotion, and behavior. Our extensive genome dataset reveals a highly dynamic demographic history with synchronous expansions and collapses on different continents during the last 400 ky after major climatic events. We show that the earliest speciation occurred with gene flow in Northern America, and that the ancestor of present-day asses and zebras dispersed into the Old World 2.1-3.4 Mya. Strikingly, we also find evidence for gene flow involving three contemporary equine species despite chromosomal numbers varying from 16 pairs to 31 pairs. These findings challenge the claim that the accumulation of chromosomal rearrangements drive complete reproductive isolation, and promote equids as a fundamental model for understanding the interplay between chromosomal structure, gene flow, and, ultimately, speciation.