Insular faunas of terrestrial mammals and bats are examined on a worldwide basis to test the adequacy of equilibrium and historical legacy models as explanations for species-area relationships. Species numbers of bats on islands conform to predictions from equilibrium theory, whereby recurrent immigrations and extinctions influence species richness. By contrast, species numbers of terrestrial mammals on islands result from a historical legacy of very low immigration rates on oceanic islands (the faunas are colonization-limited) and by the fragmentation of once contiguous continental faunas to form relictual populations, which subsequently undergo extinctions, on landbridge islands (the faunas are extinction-limited). This explanation is supported by several lines of evidence: (1) z values (slopes of species-area curves) are lower for non-volant mammals on oceanic islands than for those on landbridge islands, but are the opposite for bats; (2) z values for non-volant mammals are lower than those for bats on oceanic islands, but are higher than those for bats on landbridge islands; and (3) landbridge island faunas are attenuated mainland faunas, whereas those on oceanic islands are ecologically incomplete. No support is found for alternative hypotheses to explain low species-area slopes for terrestrial mammals on oceanic islands.