Fishes, here defined as ‘non-digitate aquatic vertebrates’, first appear in the Cambrian Period at least 520 million years ago (Ma). They are first represented by fusiform taxa lacking well-developed fins and dermal bone covering. The first fishes to bear external dermal bones forming a protective and supporting framework appear in the mid-Ordovician, about 460 Ma, represented by fusiform heterostracans and other associated taxa, found in Australia and South America. By the late Ordovician, fishes were widespread across the globe and the first jawed vertebrates, gnathostomes, had possibly appeared. The oldest gnathostome remains are enigmatic small placoid-like scales with chondrichthyan affinity, but cannot be resolved without more complete material. The oldest jawed vertebrates, both placoderms and stem chondrichthyans (‘acanthodians’), come from what is today China, with articulated diverse remains of placoderms and the first osteichthyans in the upper Silurian (Ludlow) of Yunnan. These forms include maxillate placoderms like Entelognathus and Qilinyu as well as heavily spined sarcopterygian (osteichthyan) fishes like Guiyu. At the start of the Early Devonian we see a new placoderm fish fauna emerging globally which has little resemblance to the late Silurian taxa of China, with some five main clades of placoderms and a few smaller groups of uncertain affinity. Osteichthyans diversified into two major clades, one of which, the Actinopterygii, or ray-fins, were represented by early forms with rhombic scales and fixed cheek-mouth complexes, loosely termed ‘paleoniscoids’. The Sarcopterygii, which include Actinistia (coelacanths), Dipnomorpha (dipnoans and porolepiforms), Onychodontiformes, and stem tetrapods (Tetrapodomorpha), had all appeared by the end of the early Devonian. Since the end of the Palaeozoic the non-tetrapod sarcopterygians are represented only by lungfishes and coelacanths. Chondrichthyans are known from isolated teeth, scales, and spines in the early Devonian with one articulated fish from the Emsian. By the late Devonian chondrichthyans had radiated into many families, including the first stem holocephalans, like Cladoselache. The Carboniferous saw a huge radiation of chondrichthyans and actinopterygians. Neopterygians appeared by the late Carboniferous with the first teleosteans by the late Triassic. Since the Mesozoic percomorphans especially have diversified to comprise the great majority of all fish families extant today, represented by some 29,000 spp. of teleosteans. Chondrichthyans also underwent a secondary radiation when batoids and modern sharks appeared in the Jurassic. Today there are some 1,200 species of living chondrichthyans.