As with any crown group, Mammalia is defined by extinction, and comprises all descendants of the common ancestor shared by the three synapsid lineages that happen to exist today: monotremes, marsupials, and placentals. A more inclusive, apomorphy-defined synapsid clade is Mammaliaformes, composed of all descendants of the first synapsid to evolve a functional, squamosal-dentary jaw joint. In addition to Mammalia, Mammaliaformes includes Adelobasileus, Sinoconodon, morganucodonts, docodonts, and haramiyids (see chapters by Angielczyk & Kammerer and Martin, this volume). My goal in this chapter is to outline the crown clade Mammalia, to describe its major constituents, to trace how the core ideas on mammalian evolution and interrelations have developed since the early 20th century, and to summarize how certain fossil groups are related to extant, high-level clades, with an emphasis on Placentalia.