Mixture between populations is an evolutionary process that shapes genetic variation. Intermixing between groups of distinct ancestries creates mosaics of chromosomal segments inherited from multiple ancestral populations. Studying populations of mixed ancestry (admixed populations) is of special interest in population genetics as it not only provides insights into the history of admixed groups but also affords an opportunity to reconstruct the history of the ancestral populations, some of whom may no longer exist in unmixed form. Furthermore, it improves our understanding of the impact of population migrations and helps us discover links between genetic and phenotypic variation in structured populations. The majority of research on admixed populations has focused on African Americans and Latinos where the mixture is recent, having occurred within the past 500 years. In this dissertation, I describe several studies that I have led that expand the scope of admixed studies to West Eurasians and South Asians where the mixture is older, and data from ancestral groups is mostly unavailable. First, I introduce a novel method that studies admixture linkage disequilibrium (LD) to infer the time of mixture. I analyze genomewide data from 40 West Eurasian populations and show that all Southern European, Levantine and Jewish groups have inherited sub-Saharan African ancestry in the past 100 generations, likely reflecting events during the Roman Empire and subsequent Arab migrations. Next, I apply a range of methods to study the history of Siddi groups that harbor African, Indian and Portuguese ancestry, and to infer the history of Roma gypsies from Europe. Finally, I develop a novel approach that combines the insights of frequency and LD-based statistics to infer the underlying model of mixture. I apply this method to 73 South Asian groups and infer that major mixture occurred ~2,000-4,000 years ago. In a subset of populations, all the mixture occurred during this period, a time of major change in India marked by the de- urbanization of the Indus valley civilization and recolonization of the Gangetic plateau. Inferences from our analyses provide novel insights into the history of these populations as well as about the broad impact of human migrations.