Abstract Pterosaurs are a clade of highly specialized, volant archosauromorphs recorded from the Upper Triassic to the uppermost Cretaceous. Problematic remains referred to the Pterosauria are reported from the Triassic of Europe and both North and South America, but unequivocal pterosaur specimens are only known from the Alps (Italy, Austria and Switzerland: Preondactylus buffarinii , Austriadactylus cristatus , Peteinosaurus zambellii , Eudimorphodon ranzii , Carniadactylus rosenfeldi , Caviramus schesaplanensis and Raeticodactylus filisurensis ) and Greenland (‘ Eudimorphodon’ cromptonellus ). Pterosaurs are diagnosed mostly by features associated with the advent of powered flight. They are generally considered to be archosaurians more closely related to dinosaurs than to crocodilians, but non-archosaurian positions have also been proposed. There is a lack of general agreement about ingroup relationships, particularly among the basal pterosaurs. Triassic pterosaurs differ from other non-pterodactyloid pterosaurs in features of the dentition and caudal vertebral column. A ‘Big Bang’ model for their early history fits better with the fossil record: the earliest unequivocal pterosaurs show a sudden and geographically limited appearance in the fossil record, as well as a relatively high burst of diversity and considerable morphologic disparity. Absence of pterosaur remains from deposits where they are expected to be found suggests that they had not yet evolved in pre-Norian times.