Latin Americans arguably represent the largest recently admixed populations in the world. This reflects a history of massive settlement by immigrants (mostly Europeans and Africans) and their variable admixture with Natives, starting in 1492. This process resulted in the population of Latin America showing an extensive genetic and phenotypic diversity. Here we review how genetic analyses are being applied to examine the demographic history of this population, including patterns of mating, population structure and ancestry. The admixture history of Latin America, and the resulting extensive diversity of the region, represents a natural experiment offering an advantageous setting for genetic association studies. We review how recent analyses in Latin Americans are contributing to elucidating the genetic architecture of human complex traits.