There is a period of some 5000 years or so in the prehistory of Europe when horse populations were greatly depleted and perhaps even disappeared in many places. Before this time, during the Upper Palaeolithic, wild horses were common; after, during the Bronze Age, domestic horses were being raised and used across Europe. What happened in between is uncertain, in part because of the sketchy archaeological record. Debates continue as to the origins (the when, where and how) of Europe's domestic horses, including whether horse husbandry dispersed only from habitats favourable to horses on the Eurasian steppes or whether there was local domestication in temperate Europe. This paper reviews the evidence for the transition from wild horses to domestic horses in Europe.