The marsupial and placental mammals originated at a time when the pattern of geographical barriers (oceans, shallow seas and mountains) was very different from that of today, and climates were warmer. The sequence of changes in these barriers, and their effects on the dispersal of the mammal families and on the faunas of mammals in the different continents, are reviewed. The mammal fauna of South America changed greatly in the Pliocene/Pleistocene, when the newly-complete Panama Isthmus allowed the North American fauna to enter the continent and replace most of the former South American mammal families. Marsupial, but not placental, mammals reached Australia via Antarctica before Australia became isolated, while rats and bats are the only placentals that dispersed naturally from Asia to Australia in the late Cenozoic. Little is known of the early history of the mammal fauna of India. A few mammal families reached Madagascar from Africa in the early Cenozoic over a chain of islands. Africa was isolated for much of the early Cenozoic, though some groups did succeed in entering from Europe. Before the climate cooled in the mid-Cenozoic, the mammal faunas of the Northern Hemisphere were much richer than those of today.