The fundamental shift associated with the domestication of plants and animals allowed for a dramatic increase in human population sizes and the emergence of modern society. Despite its importance and the decades of research devoted to studying it, questions regarding the origins and processes of domestication remain. Here, we review recent theoretical advances and present a perspective that underscores the crucial role that population admixture has played in influencing the genomes of domestic animals over the past 10000 years. We then discuss novel approaches to generating and analysing genetic data, emphasising the importance of an explicit hypothesis-testing approach for the inference of the origins and subsequent evolution and demography of domestic animals. By applying next-generation sequencing technology alongside appropriate biostatistical methodologies, a substantially deeper understanding of domestication is on the horizon. Copyright © 2013 Elsevier Ltd. All rights reserved.