The chapter discusses the significant movements and replacements of human populations that occurred due to the rise of food production around the world, particularly after the end of the Ice Ages. The first farming societies gained advantages over hunter-gatherer societies, leading to the expansion and replacement of these latter groups with farmers and their languages. The authors highlight the complexity and controversy surrounding these expansions, emphasizing the need for interdisciplinary research that combines archaeology, crop and livestock studies, physical anthropology, genetics, and linguistics. The basic hypothesis suggests that prehistoric agriculture dispersed hand-in-hand with human genes and languages, but this hypothesis is often controversial due to the lack of concordance between genetic, archaeological, linguistic, and skeletal evidence. The main complications include genetic admixture between hunter-gatherers and farmers, adoption of farming by peripheral hunter-gatherers, reversion to hunter-gatherer lifestyles by expanding farmers, language shift by indigenous populations, and replacement of the expanding farmers' language in their original homeland. The chapter also examines specific examples of language family expansions, such as the Bantu, Arawak, Austro-Asiatic, Tai, Sino-Tibetan, Uto-Aztecan, Oto-Manguean, Mayan, and Austronesian languages, among others. Each example is analyzed in terms of the evidence supporting the hypothesis and the complexities involved. Finally, the authors call for new evidence and interdisciplinary research to resolve the many controversies in this field, emphasizing the importance of understanding how genetic data should be interpreted in terms of human history. They also highlight the need for more studies of languages themselves and the environmental factors that influenced the expansion of early farmers.The chapter discusses the significant movements and replacements of human populations that occurred due to the rise of food production around the world, particularly after the end of the Ice Ages. The first farming societies gained advantages over hunter-gatherer societies, leading to the expansion and replacement of these latter groups with farmers and their languages. The authors highlight the complexity and controversy surrounding these expansions, emphasizing the need for interdisciplinary research that combines archaeology, crop and livestock studies, physical anthropology, genetics, and linguistics. The basic hypothesis suggests that prehistoric agriculture dispersed hand-in-hand with human genes and languages, but this hypothesis is often controversial due to the lack of concordance between genetic, archaeological, linguistic, and skeletal evidence. The main complications include genetic admixture between hunter-gatherers and farmers, adoption of farming by peripheral hunter-gatherers, reversion to hunter-gatherer lifestyles by expanding farmers, language shift by indigenous populations, and replacement of the expanding farmers' language in their original homeland. The chapter also examines specific examples of language family expansions, such as the Bantu, Arawak, Austro-Asiatic, Tai, Sino-Tibetan, Uto-Aztecan, Oto-Manguean, Mayan, and Austronesian languages, among others. Each example is analyzed in terms of the evidence supporting the hypothesis and the complexities involved. Finally, the authors call for new evidence and interdisciplinary research to resolve the many controversies in this field, emphasizing the importance of understanding how genetic data should be interpreted in terms of human history. They also highlight the need for more studies of languages themselves and the environmental factors that influenced the expansion of early farmers.