Th e fossil record of lungfi sh is reviewed. Some of their unique characteristics are explained and illustrated, including some less well-known anatomical elements that are oft en misidentifi ed or unidentifi ed in museum collections of Paleozoic vertebrates. Lungfi sh records from the Early Devonian to the Late Mesozoic are illustrated and described chronologically. Th eir major diversifi cation occurred during the Devonian Period, with more than 70 named species. Subsequently they declined in diversity during the Carboniferous and Permian to a low of three genera at the present day. Some Carboniferous and Permian forms show intermediate morphologies between the Late Devonian and Mesozoic forms. Some of the intriguing questions of lungfi sh biology that can be addressed from the fossil record are outlined, such as the modifi cation of their skeletons from a more or less primitive sarcopterygian pattern to their specialised form with loss of cosmine on bones and scales, few dermal skull bones, continuous mid-line fi ns and reduction of the paired fi ns to narrow, whip-like appendages. Late Devonian and Carboniferous lungfi sh are frequently found associated with tetrapods, and several lungfi sh anatomical elements are sometimes mistaken for those of tetrapods. Th e reduction in ossifi cation of lungfi sh skeletons creates problems for understanding their fossil record: it may be explicable in terms of retention of a juvenile state. Reduction

in ossifi cation takes place alongside increase in the genome size: it has been suggested that these two phenomena may be related. Th eir varied patterns of dentition may be explicable by the interaction of only a few developmental processes, but the present pattern had been established by the Devonian. Th e evolution of air-breathing, aestivation, biogeographical distribution and change in habitat from fully marine during the Early Devonian to entirely freshwater at present are reviewed. Keywords: evolutionary history, anatomy, Devonian, Palaeozoic, Mesozoic, Cenozoic.