Abstract Fossil chondrichthyan teeth played an important part in the establishment of a scientific understanding of ‘formed stones’. Following a slowly emerging taxonomy, Louis Agassiz presented the first comprehensive guide to Palaeozoic chondrichthyans in the 1830s. The next contribution of any substance was Arthur Smith Woodward’s Catalogue of Fossil Fishes in the British Museum (Natural History) with a historical, descriptive and systematic review of the chondrichthyans, a group on which he already had an impressively large publication record. Initially stimulated by his observations on an articulated petalodont dentition ( Climaxodus ), Smith Woodward erected the Bradyodonti in 1921. Defined on the possession of dentitions with very slow growth rates, only seven or eight successional teeth produced throughout the lifetime of the fish, and retention rather than shedding of earlier teeth, primarily by fusion to later ones, the bradyodonts embraced petalodonts, psammodonts, copodonts and cochliodonts. The establishment and subsequent demise of the bradyodonts is briefly reviewed here.