During the Trans-Atlantic Slave Trade (TAST), around twelve million Africans were enslaved and forcibly moved from Africa to the Americas and Europe, durably influencing the genetic and cultural landscape of a large part of humanity since the 15th century. Following historians, archaeologists, and anthropologists, population geneticists have, since the 1950’s mainly, extensively investigated the genetic diversity of populations on both sides of the Atlantic. These studies shed new lights into the largely unknown genetic origins of numerous enslaved-African descendant communities in the Americas, by inferring their genetic relationships with extant African, European, and Native American populations. Furthermore, exploring genome-wide data with novel statistical and bioinformatics methods, population geneticists have been increasingly able to infer the last 500 years of admixture histories of these populations. These inferences have highlighted the diversity of histories experienced by enslaved-African descendants, and the complex influences of socio-economic, political, and historical contexts on human genetic diversity patterns during and after the slave trade. Finally, the recent advances of paleogenomics unveiled crucial aspects of the life and health of the first generation of enslaved Africans in the Americas. Altogether, human population genetics approaches in the genomic and paleogenomic era need to be coupled with history, archaeology, anthropology, and demography in interdisciplinary research, to reconstruct the multifaceted and largely unknown history of the TAST and its influence on human biological and cultural diversities today. Here, we review anthropological genomics studies published over the past 15 years and focusing on the history of enslaved-African descendant populations in the Americas.