The Subclass Elasmobranchii is widely considered nowadays to be the sister group of the Subclass Holocephali, although chimaeroid fishes were originally classified as elasmobranchs along with modern sharks and rays. While this modern systematic treatment provides an accurate reflection of the phylogenetic relationships among extant taxa, the classification of many extinct non-holocephalan shark-like chondrichthyans as elasmobranchs is challenged. A revised, apomorphy-based definition of elasmobranchs is presented in which they are considered the equivalent of neoselachians, i.e. a monophyletic group of modern sharks and rays which not only excludes all stem and crown holocephalans, but also many Palaeozoic shark-like chondrichthyans and even close extinct relatives of neoselachians such as hybodonts. The fossil record of elasmobranchs (i.e. neoselachians) is reviewed, focusing not only on their earliest records but also on their subsequent distribution patterns through time. The value and limitations of the fossil record in answering questions about elasmobranch phylogeny are discussed. Extinction is seen as a major factor in shaping early elasmobranch history, especially during the Triassic. Extinctions may also have helped shape modern lamniform diversity, despite uncertainties surrounding the phylogenetic affinities of supposedly extinct clades such as cretoxyrhinids, anacoracids and odontids. Apart from these examples, and the supposed Cretaceous extinction of ‘sclerorhynchids’, elasmobranch evolution since the Jurassic has mostly involved increased diversification (especially during the Cretaceous). The biogeographical distribution of early elasmobranchs may be obscured by sampling bias, but the earliest records of numerous groups are located within the Tethyan realm. The break-up of Gondwana, and particularly the opening of the South Atlantic Ocean (together with the development of epicontinental seaways across Brazil and Africa during the Cretaceous), provided repeated opportunities for dispersal from both eastern (European) and western (Caribbean) Tethys into newly formed ocean basins.