Major progress in understanding biological invasions has recently been made by quantitatively comparing successful and unsuccessful invasions. We used such an approach to test hypotheses about the role of climatic suitability, life history, and historical factors in the establishment and subsequent spread of 40 species of mammal that have been introduced to mainland Australia. Relative to failed species, the 23 species that became established had a greater area of climatically suitable habitat available in Australia, had previously become established elsewhere, had a larger overseas range, and were introduced more times. These relationships held after phylogeny was controlled for, but successful species were also significantly more likely to be nonmigratory. A forward-selection model included only two of the nine variables for which we had data for all species: climatic suitability and introduction effort. When the model was adjusted for phylogeny, those same two variables were included, along with previous establishment success. Of the established species, those with a larger geographic range size in Australia had a greater area of climatically suitable habitat, had traits associated with a faster population growth rate (small body size, shorter life span, lower weaning age, more offspring per year), were nonherbivorous, and had a larger overseas range size. When the model was adjusted for phylogeny, the importance of climatic suitability and the life-history traits remained significant, but overseas range size was no longer important and species with greater introduction effort had a larger geographic range size. Two variables explained variation in geographic range size in a forward-selection model: species with smaller body mass and greater longevity tended to have larger range sizes in Australia. These results mirror those from a recent analysis of exotic-bird introductions into Australia, suggesting that, at least among vertebrate taxa, similar factors predict establishment and spread. Our approach and results are being used to assess the risks of exotic vertebrates becoming established and spreading in Australia.