Besides its obvious intrinsic value, knowledge of population history, and of the demographic and evolutionary changes that accompany it, has proven fundamental to address applied research in human genetics. In this review we place current European genetic diversity in the context of the global human genome diversity and review the evidence supporting a recent African origin of the Europeans. We then discuss the results and the interpretation of genetic studies attempting to quantify the relative importance of various gene flow processes, both within Europe and from Asia into Europe, focusing especially on the initial, Paleolithic colonization of the continent, and on later, Paleolithic postglacial and Neolithic dispersals. Finally, we discuss how knowledge of the patterns of genetic diversity in Europe, and of their inferred generating processes, can be extremely useful in planning health care and in biomedical research.