For several decades, the origin of domestic horses has been the focus of research across multiple disciplines, yet many aspects of the horse domestication process remain poorly understood. One of the reasons for the difficulty in establishing a coherent scenario of horse domestication is that archaeological, mtDNA, and Y chromosome data have yielded ambiguous results, possibly because each class of markers reflects different aspects of the domestication process. In this thesis, I use large autosomal genetic datasets from horses sampled across Eurasia to investigate the origin and spread of horse domestication. I begin by characterising genetic diversity of horses from the Eurasian steppes and neighbouring regions, thus laying the groundwork for a more thorough analysis into the demographic history of horses. I then investigate the origin and mode of spread of horse domestication in the Eurasian steppe region using a spatially explicit genetic model. I show that horse domestication was initiated in the western part of the steppes, and that the spread of horse domestication involved both movement of domestic herds and extensive recruitment of wild horses from across this vast region, a scenario which integrates both archaeological and molecular evidence. Having established the route of spread of early domestic horses out of their domestication origin in the western steppe, I go on to investigate the routes and levels of gene flow among Eastern Eurasian horse populations post-domestication. I show that the ancient Silk Roads have played an important role in shaping the genetic structure of Eastern Eurasian horses, facilitating gene flow across deserts and high mountain chains. Finally, I provide further compelling evidence for the persistence of wild horses in the Iberian Peninsula throughout the Holocene period, and the substantial contribution of these local populations to the gene pool of Iberian domestic horses. Together, my results provide a coherent picture of the origin and spread of horse domestication, integrating for the first time previous evidence from archaeology, mtDNA and Y chromosome sequence data.