To halt the spread of invasive species and reduce their impact on native taxa, we need a better understanding of the dynamics and determinants of range expansion in exotic habitats.  Classical diffusion theory predicts that invasions will progress at a constant rate until they reach the boundaries of the species’ conserved ancestral niche in the new environment.  However, the assumptions underlying these predictions may often be violated.  We evaluated the environmental correlates of the cane toad’s (Bufo marinus) invasion of Australia through time and space.  Our results indicate that toads have expanded their range into areas previously thought to be uninhabitable based on their native distribution.  Most of the expansion in suitable habitat area has occurred in the last decade and in regions characterized by hot temperatures.  Moreover, results suggest that cane toads have accelerated their range expansion into regions of northern Australia while expansions into other regions have progressed at a linear rate.  The accelerating invasion in northern subtropical regions likely has resulted from adaptations for faster dispersal and from environmental conditions that have facilitated the toads’ advance.  The toads’ increasing use of extreme habitats may indicate that novel ecological conditions in the absence of native species interactions have facilitated a broader realized niche or that toad populations at the invasion front have evolved a greater tolerance to extreme abiotic conditions.  Ecological release from native enemies combined with rapid evolution in novel habitats provides insights into how some species become highly successful global invaders.