The human capacity to acquire complex language seems to be without parallel in the natural world. The origins of this remarkable trait have long resisted adequate explanation, but advances in fields that range from molecular genetics to cognitive neuroscience offer new promise. Here we synthesize recent developments in linguistics, psychology and neuroimaging with progress in comparative genomics, gene-expression profiling and studies of developmental disorders. We argue that language should be viewed not as a wholesale innovation, but as a complex reconfiguration of ancestral systems that have been adapted in evolutionarily novel ways.