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. Whole-genome analysis of the elephant shark, a cartilaginous fish, shows that it is the slowest evolving of all known vertebrates, lacks critical bone formation genes and has an unusual adaptive immune system. The elephant shark (Callorhinchus milii) is a cartilaginous fish native to the temperate waters off southern Australia and New Zealand, living at depths of 200 to 500 metres and migrating into shallow waters during spring for breeding. The genome sequence is published in this issue of Nature. Comparison with other vertebrate genomes shows that it is the slowest evolving genome of all known vertebrates — coelacanth included. Genome analysis points to an unusual adaptive immune system lacking the CD4 receptor and some associated cytokines, indicating that cartilaginous fishes possess a primordial gnathostome adaptive immune system. Also absent are genes encoding secreted calcium-binding phosphoproteins, in line with the absence of bone in cartilaginous fish.