Background/Aims: The genetic diversity of Europeans has been shaped by various evolutionary forces including their demographic history. Genetic data can thus be used to draw inferences on the population history of Europe using appropriate statistical methods such as computer simulation, which constitutes a powerful tool to study complex models. Methods: Here, we focus on spatially explicit simulation, a method which takes population movements over space and time into account. We present its main principles and then describe a series of studies using this approach that we consider as particularly significant in the context of European prehistory. Results and Conclusion: All simulation studies agree that ancient demographic events played a significant role in the establishment of the European gene pool; but while earlier works support a major genetic input from the Near East during the Neolithic transition, the most recent ones revalue positively the contribution of pre-Neolithic hunter-gatherers and suggest a possible impact of very ancient demographic events. This result of a substantial genetic continuity from pre-Neolithic times to the present challenges some recent studies analyzing ancient DNA. We discuss the possible reasons for this discrepancy and identify future lines of investigation in order to get a better understanding of European evolution.