Reconstructing the evolutionary relationships among the orders of eutherian mammals constitutes a formidable phylogenetic task. It entails the identification of a single true phylogenetic tree out of 1012-1028 possible ones. For almost half a century, the field of mammalian Phylogeny has been dominated by a pessimistic view, according to which the great burst of mammalian radiations more than 65 million years ago has rendered the ordinal phylogeny of mammals insolvable. In the last few years, this pessimism has started to dissipate as several superordinal relationships were identified through the use of molecular data. DNA and protein sequences have the potential to supply millions of phyloge netically useful characters, and therefore, the Phylogeny of the orders of mammals may be resolved into a consistently bifurcating tree in the not-sodistant future.