Understanding the introduction of farming and the adoption of Neolithic culture continues to be a major research objective in Europe. The authors make use of a new database of radiocarbon dates from Mesolithic and Neolithic sites to map the transition. While the overall effect is still a diffusion into Europe from the south-east, detailed spatial analysis reveals fascinating local variations: in some places change was rapid, and one population replaced another, in others it was gradual and owed to incoming ideas rather than people.