One of the biggest innovations in human prehistory was the advent of food production, consisting of the ability to grow crops and domesticate animals for consumption. This wide-scale transition from hunting and gathering to food production led to more permanent settlements, and set in motion major societal changes. In western Eurasia, this revolution spread from the Near East into Europe, Africa and diverse regions of Asia. Agriculture was brought into Europe by the descendants of early Anatolian farmers starting approximately 8,000 years ago. But little was known of the people who developed agriculture in the Fertile Crescent: where they all closely related to the early Anatolian farmers, or were there multiple ethnic groups who developed agriculture in parallel? In the first data chapter, I use the first genome from a Neolithic woman from Ganj Dareh, in the Zagros Mountains (Iran), a site with evidence of early goat domestication 10,000 years ago. I showed that Western Iran wan inhabited by populations mostly similar to Hunter- gatherer populations from the Caucasus, but remarkably, very distinct from the Anatolian farmers who spread the Neolithic package into Europe. While a degree of cultural diffusion between Anatolia, Mesopotamia and the Zagros highlands likely happened, genetic dissimilarity supports a model in which Neolithic societies of that area were distinct. The second chapter deals with how Africa was affected by population movements, originating in the Near East, during the Neolithic times. Characterising genetic diversity in Africa is a crucial step for analyses reconstructing human evolution. Using Mota, an ancient genome from a male from the Ethiopian highlands, I showed a backflow into Africa by populations closely related to the Anatolian Neolithic farmers. The third chapter deals with some common problems and themes in the analysis of ancient DNA, such as merging capture datasets with diverse number of ascertained SNPs, combining capture and shotgun data in the same analysis, and the effect of UDG treatment in ancient samples. I describe the most common problems and their effect in summary statistics, and propose a guide on how to work with ancient DNA to avoid data compatibility problems.