This paper reviews the state-of-the-art knowledge concerning the relationship between Neanderthals and Upper Paleolithic modern humans. The branching-process method is applied to infer the upper limit of hypothetical Neanderthal admixture, consistent with the evidence based on mitochon- drial DNA sequences of contemporary modern humans, as well as Neanderthal and early modern European H. sapiens fossils. As a result, a maximum value of 15% admixture is obtained. This estimate is discussed in the context of its consequences for the two competing theories of modern human origin.