The evolutionary processes underlying range expansion is a fundamental question in evolutionary biology. Range limits of a species are set by both abiotic and biotic factors, and these limits are constantly in flux. Here, I use genetic data to examine the consequences of range expansion at both deep evolutionary scales (millions of years), and microevolutionary scales (tens of generations), using amphibians as a model system. In the first chapter, I use phylogenetic analyses to examine the drivers of diversification in a neotropical genus of treefrogs (Boana). I find that at the continental scale changes to topography, and climatic oscillations interacted to facilitate range expansion, and subsequent speciation of frogs inhabiting distinct biomes in South America. In chapters two, three, and four, I use the introduced species, the cane toad (Rhinella marina) to investigate rapid adaptation during range expansion. In chapter two, I use experimental physiology to demonstrate that cane toads at the northern Florida range edge are more tolerant of cold temperatures, suggesting that rapid adaptation may facilitate range-expansion in the coldest place cane toads are found. In chapter three, I examine the global context of cane toad introductions in the USA and Caribbean using next-generation sequencing to compare and contrast demographic history and selection across the native range, and parallel introductions. I find evidence for some parallel adaptations across introductions, as well as signatures of historical admixture, which may have increased genetic diversity in introductions. In chapter four, I focus on the introduction of cane toads to Florida, USA. I find signatures of selection associated with environmental gradients across the range, and population structure consistent with a singular introduction and subsequent range-expansion into cooler, drier environments. Thus, the maintenance of genetic diversity following introduction, and adaptation to novel conditions appear to facilitate the spread of this species over short time scales. Understanding the evolutionary processes at range-edges is critical both for the field of evolutionary biology, as well as for the conservation of the many organisms expected to face novel environmental conditions due to climate change.