Farming was first introduced to southeastern Europe in the mid-7th millennium BCE - brought by migrants from Anatolia who settled in the region before spreading throughout Europe. However, the dynamics of the interaction between the first farmers and the indigenous hunter-gatherers remain poorly understood because of the near absence of ancient DNA from the region. We report new genome-wide ancient DNA data from 204 individuals-65 Paleolithic and Mesolithic, 93 Neolithic, and 46 Copper, Bronze and Iron Age-who lived in southeastern Europe and surrounding regions between about 12,000 and 500 BCE. We document that the hunter-gatherer populations of southeastern Europe, the Baltic, and the North Pontic Steppe were distinctive from those of western Europe, with a West-East cline of ancestry. We show that the people who brought farming to Europe were not part of a single population, as early farmers from southern Greece are not descended from the Neolithic population of northwestern Anatolia that was ancestral to all other European farmers. The ancestors of the first farmers of northern and western Europe passed through southeastern Europe with limited admixture with local hunter-gatherers, but we show that some groups that remained in the region mixed extensively with local hunter-gatherers, with relatively sex-balanced admixture compared to the male-biased hunter-gatherer admixture that we show prevailed later in the North and West. After the spread of farming, southeastern Europe continued to be a nexus between East and West, with intermittent steppe ancestry, including in individuals from the Varna I cemetery and associated with the Cucuteni-Trypillian archaeological complex, up to 2,000 years before the Steppe migration that replaced much of northern Europe's population.