The emergence of jawed vertebrates (gnathostomes) from jawless vertebrates was accompanied by major morphological and physiological innovations, such as hinged jaws, paired fins and immunoglobulin-based adaptive immunity. Gnathostomes subsequently diverged into two groups, the cartilaginous fishes and the bony vertebrates. Here we report the whole-genome analysis of a cartilaginous fish, the elephant shark (Callorhinchus milii). We find that the C. milii genome is the slowest evolving of all known vertebrates, including the 'living fossil' coelacanth, and features extensive synteny conservation with tetrapod genomes, making it a good model for comparative analyses of gnathostome genomes. Our functional studies suggest that the lack of genes encoding secreted calcium-binding phosphoproteins in cartilaginous fishes explains the absence of bone in their endoskeleton. Furthermore, the adaptive immune system of cartilaginous fishes is unusual: it lacks the canonical CD4 co-receptor and most transcription factors, cytokines and cytokine receptors related to the CD4 lineage, despite the presence of polymorphic major histocompatibility complex class II molecules. It thus presents a new model for understanding the origin of adaptive immunity.