The process of biological invasion exposes a species to novel pressures, both in terms of the environments it encounters and the evolutionary consequences of range expansion. Several invaders have been shown to exhibit rapid evolutionary changes in response to those pressures, thus providing robust opportunities to clarify the processes at work during rapid phenotypic transitions. The accelerating pace of invasion of cane toads (Rhinella marina) in tropical Australia during its 80-year history has been well-characterised at the phenotypic level, including common-garden experiments that demonstrate heritability of several dispersal-relevant traits. Individuals from the invasion front (and their progeny) show distinctive changes in morphology, physiology and behaviour that (in combination) result in far more rapid dispersal than is true of conspecifics from long-colonised areas. Remarkably, studies of neutral markers show extremely limited genetic diversity in this population. Here we discuss our analyses of differential gene expression in toads from both ends of this invasion-history transect; we have found substantial up-regulation of many genes on the invasion front, notably those involved in metabolism and cellular repair. Gene ontology enrichment analysis confirms the importance of genes underlying energy production and responses to environmental stressors in individuals from the range edge. Such pronounced phenotypic and gene expression differences in a population with extremely limited genetic diversity suggest a possible role for epigenetic control of these traits. We discuss these possibilities and our approach to teasing apart mechanisms underlying rapid evolution in this population.