Between ca. 50,000 and 40,000 years ago, one of the most profound upheavals in the history of humanity occurred with the extinction of Neanderthals and the emergence of anatomically modern humans (Homo sapiens) in Europe. The main paradigm over the last 30 years characterized this process as a simple population replacement, considering Neanderthals and Sapiens as distinct at the species level. Here, I review the genetic, paleoanthropological and archaeological data and try to show that they support an assimilation model with major interbreeding and converging cultural developments towards the independent adoption of what is called the “Upper Palaeolithic package” including symbolic material culture and art.