This is a review of genetic evidence about the ancient demography of the ancestors of our species and about the genesis of worldwide human diversity. The issue of whether or not a population size bottleneck occurred among our ancestors is under debate among geneticists as well as among anthropologists. The bottleneck, if it occurred, would confirm the Garden of Eden (GOE) model of the origin of modern humans. The competing model, multiregional evolution (MRE), posits that the number of human ancestors has been large, occupying much of the temperate Old World for the last two million years. While several classes of genetic marker seem to contain a strong signal of demographic recovery from a small number of ancestors, other nuclear loci show no such signal. The pattern at these loci is compatible with the existence of widespread balancing selection in humans. The study of human diversity at (putatively) neutral genetic marker loci has been hampered since the beginning by ascertainment bias since they were discovered in Europeans. The high levels of polymorphism at microsatellite loci means that they are free of this bias. Microsatellites exhibit a clear almost linear diversity gradient away from Africa, so that New World populations are approximately 15% less diverse than African populations. This pattern is not compatible with a model of a single large population expansion and colonization of most of the Earth by our ancestors but suggests, instead, gradual loss of diversity in successive colonization bottlenecks as our species grew and spread.