Tasmanian devils (Sarcophilus harrisii) are evolving in response to a unique transmissible cancer, devil facial tumour disease (DFTD), first described in 1996. Persistence of wild populations and the recent emergence of a second independently evolved transmissible cancer suggest that transmissible cancers may be a recurrent feature in devils. We used a targeted sequencing approach, RAD-capture, to identify genomic regions subject to rapid evolution in approximately 2,500 devils as DFTD spread across the species range. We found evidence for genome-wide contemporary evolution, including 186 candidate genes related to cell cycling and immune response. We then searched for signatures of recurrent selection with a molecular evolution approach and found widespread evidence of historical positive selection in devils relative to other marsupials. We identified both contemporary and historical selection in 19 genes and enrichment for contemporary and historical selection independently in 22 gene sets. Nonetheless, the overlap between candidates for historical selection and for contemporary response to DFTD was lower than expected, supporting novelty in the evolutionary response of devils to DFTD. Our results can inform management actions to conserve adaptive capacity of devils by identifying high priority targets for genetic monitoring and maintenance of functional diversity in managed populations.