The migration into and settlement of remote Oceania by the modern Polynesian and Māori peoples is a major achievement, which has been the subject of extensive research and scholarship. The routes taken by the Austronesian peoples and the origins of the migrations are subject to ongoing debate. We present a range of findings from molecular genetic studies of Polynesian and New Zealand Māori populations and a ‘synthetic total evidence theory’ that we suggest can account for key elements of the migrations.