The origin and evolution of hominoid primates (apes and man) has long been studied exclusively on the basis of available fossil remains. Indeed, a migration of African primates towards Asia at about −16 to −17 Ma might have given the lineage of Miocene Asian hominoids. This hypothesis is supported by the oldest remains of Miocene Asian hominoids dated at about −16.1 Ma. But the recent discovery of anthropoid primates in the Eocene of Asia seems to indicate that Asia was a major evolutionary and differentiation centre for anthropoid primates as early as the Eocene. In addition, Asian primates probably continued to evolve in Asia from the Eocene onward and led at least to the extant Asian hominoids (orangutans and gibbons). African and Asian extant anthropoid primates might therefore have diverged at least 36 Ma ago, and this hypothesis is also supported by the most recent data in molecular biology. Moreover, an Asiatic origin of African Paleogene propliopithecine primates is suggested. In that context, evolutionary rates might not be constant, and molecular clocks should be necessarily characteristic for each studied group of mammals. Several examples that illustrate the conflict between paleontological and molecular data are discussed. The necessity to integrate more systematically paleontological data as chronological reference points in studies in molecular phylogeny is discussed.