Darwin's finches, inhabiting the Galápagos archipelago and Cocos Island, constitute an iconic model for studies of speciation and adaptive evolution. Here we report the results of whole-genome re-sequencing of 120 individuals representing all of the Darwin's finch species and two close relatives. Phylogenetic analysis reveals important discrepancies with the phenotype-based taxonomy. We find extensive evidence for interspecific gene flow throughout the radiation. Hybridization has given rise to species of mixed ancestry. A 240 kilobase haplotype encompassing the ALX1 gene that encodes a transcription factor affecting craniofacial development is strongly associated with beak shape diversity across Darwin's finch species as well as within the medium ground finch (Geospiza fortis), a species that has undergone rapid evolution of beak shape in response to environmental changes. The ALX1 haplotype has contributed to diversification of beak shapes among the Darwin's finches and, thereby, to an expanded utilization of food resources.