For over a decade there has been general, but not universal, consensus that the earliest known evidence for horse husbandry was at Eneolithic Botai, Kazakhstan, circa 3,500 BCE. Recent ancient genomic analyses, however, indicate that Botai is not the source of modern domestic horse stock (DOM2 lineage), but is instead related to the Przewalski clade of horses. DOM2 appears to instead to have emerged in early Bronze Age (mid 3rd Mill. BCE) in the Pontic-Caspian steppe, and spread quickly replacing other horse lineages after approximately 2,000 BCE. Whilst the specific evidence for earlier husbandry at Botai is not diminished by this evidence, it has broken the consensus regarding the early stages of horse domestication, with some now viewing it as a later event. This paper argues that domestication is rarely an event, but instead a process that is ongoing. The case is made for a “prey pathway” initial phase of domestication in multiple localities during the Eneolithic, which was based around local subsistence pastoralist niche construction. This took different forms due to the presence or absence of ruminant domestic stock in the Eastern European or Central Asian steppes, respectively. Whilst “push” factors likely played a part in the development of horse specialist pastoralism at Botai, it is suggested that “pull” factors accelerated the spread of DOM2 lineages, replacing others, in the later Bronze Age. The DOM2 spread was principally driven, not by local subsistence needs, but wider social, economic and military desirability of equestrianism. The long-term process of horse domestication continues in modernity with major breed changes caused first by the post-medieval agricultural revolution and, more currently, the desire for sporting achievement.