More than two decades after its publication, MacArthur and Wilson's equilibrium model of insular biogeography continues to provide the conceptual foundation for investigating the distribution of species on islands and the composition of insular biotas. During this period, studies of the distributions of mammals among insular habitats have tested, modified, and extended MacArthur and Wilson's simple formalism to enhance greatly our understanding of the complexities of biogeographic patterns and processes. The papers in this symposium summarize many of the past contributions of mammalian biogeographers and introduce important new data and ideas. The diversity of biological characteristics and associated distributional patterns exhibited by mammals has facilitated this endeavour. Some insular mammalian faunas appear to represent approximate equilibria between opposing rates of contemporary colonization and extinction. Other faunas are currently decreasing in diversity because of extinctions, owing either to natural habitat fragmentation that has occurred since the Pleistocene or to human activities within the last few centuries. Still other faunas have been increasing in diversity (at least until recent human impacts) because limiting rates of origination, both colonization and speciation, have been extremely low. The questions and analyses of island biogeography can also be applied to continents with comparable overall results: the distributions of continental faunas reflect the consequences of similar processes of colonization, speciation and extinction. Analyses of insular distributions show unequivocally that probabilities of extinction, colonization and speciation are highly deterministic and vary in predictable ways among different taxa and archipelagos. These findings have important implications for applying the theory and data of insular biogeography to the pressing practical problems of designing natural reserves to preserve native species.