Darwin’s finches from the Galápagos archipelago have historic importance in the field of evolutionary biology as they provided some of the fundamental insights into processes of natural selection and adaptive radiation. Evolution in Darwin’s finches is characterized by rapid adaptation to an unstable and challenging environment leading to ecological diversification and speciation. This has resulted in striking diversity in their phenotypes (for instance, beak types, body size, plumage, feeding behavior and song types). Beaks are one of the most diversified features in these birds and are well adapted to the type of food they eat; ranging from fine needle-like beaks in warbler finches that are perfect for picking up insects; long, sharp and pointed beaks in cactus finches for probing into cactus or deep, broad and blunt beaks in large ground finches suited for cracking large nuts and seeds. We sequenced the genomes of multiple individuals (n=180) from all species of Darwin’s finches and their close relatives. The genome analysis indicated extensive evidence of interspecies gene flow across the entire radiation and identified cases where hybridization gave rise to species of mixed ancestry. The results highlighted interspecies hybridization being crucial in maintaining genetic diversity and possibly played a critical role during the evolution of finches. We also compared the genomes of species with blunt and pointed beaks and identified ALX1 gene affecting craniofacial development to be strongly associated with variation in beak shape. The variants of ALX1 differed not only between the species with varying beak shapes, but also among individuals of medium ground finch, a species that has undergone rapid evolution of beak shape in response to environmental changes. We also investigated the genetics underlying a previously documented evolutionary change where beak sizes of one population of medium ground finches became smaller in response to a drought-induced food shortage due to strong natural selection. We identified HMGA2 gene varies systematically between species with different beak sizes. The large beak HMGA2 variant was more common in birds that died during the episode of drought, while small beak variant was common in those birds that survived. The results indicated that diversity in HMGA2 gene allowed for a rapid evolution of smaller beak size in medium ground finch, thereby providing an evidence of a gene behind ‘evolution in action’ recorded in real time.