The fossil record of tetrapods is very patchy because of the problems of preservation, in terrestrial sediments in particular, and because vertebrates are rarely very abundant. However, the fossil record of tetrapods has the advantages that it is easier to establish a phylogenetic taxonomy than for many invertebrate groups, and there is the potential for more detailed ecological analyses. The relative incompleteness of a fossil record may be assessed readily, and this can be used to test whether drops in overall diversity are related to mass extinctions or to gaps in our knowledge. Absolute incompleteness cannot be assessed directly, but a historical approach may offer clues to future improvements in our knowledge. One of the key problems facing palaeobiologists is paraphyly, the fact that many higher taxa in common use do not contain all of the descendants of the common ancestor. This may be overcome by cladistic analysis and the identification of monophyletic groups. The diversity of tetrapods increased from the Devonian to the Permian, remained roughly constant during the Mesozoic, and then began to increase in the late Cretaceous, and continued to do so during the Tertiary. The rapid radiation of 'modern' tetrapod groups--frogs, salamanders, lizards, snakes, turtles, crocodilians, birds and mammals--was hardly affected by the celebrated end-Cretaceous extinction event. Major mass extinctions among tetrapods took place in the early Permian, late Permian, early Triassic, late Triassic, late Cretaceous, early Oligocene and late Miocene. Many of these events appear to coincide with the major mass extinctions among marine invertebrates, but the tetrapod record is largely equivocal with regard to the theory of periodicity of mass extinctions.