In this paper I propose that evolutionary demography and associated theory from human behavioral ecology provide a strong basis for explaining the available evidence for the patterns observed in the first agricultural settlement of Europe in the 7th–5th millennium cal. BC, linking together a variety of what have previously been disconnected observations and casting doubt on some long-standing existing models. An outline of relevant aspects of life history theory, which provides the foundation for understanding demography, is followed by a review of large-scale demographic patterns in the early Neolithic, which point to rapid population increase and a process of demic diffusion. More localized socioeconomic and demographic patterns suggesting rapid expansion to local carrying capacities and an associated growth of inequality in the earliest farming communities of central Europe (the Linear Pottery Culture, or LBK) are then outlined and shown to correspond to predictions of spatial population ecology and reproductive skew theory. Existing models of why it took so long for farming to spread to northern and northwest Europe, which explain the spread in terms of the gradual disruption of hunter-gatherer ways of life, are then questioned in light of evidence for population collapse at the end of the LBK. Finally, some broader implications of the study are presented, including the suggestion that the pattern of an initial agricultural boom followed by a bust may be relevant in other parts of the world.