The rise of archosaurs during the Triassic and Early Jurassic has been treated as a classic example of an evolutionary radiation in the fossil record. This paper reviews published studies and provides new data on archosaur lineage origination, diversity and lineage evolution, morphological disparity, rates of morphological character change, and faunal abundance during the Triassic–Early Jurassic. The fundamental archosaur lineages originated early in the Triassic, in concert with the highest rates of character change. Disparity and diversity peaked later, during the Norian, but the most significant increase in disparity occurred before maximum diversity. Archosaurs were rare components of Early–Middle Triassic faunas, but were more abundant in the Late Triassic and pre-eminent globally by the Early Jurassic. The archosaur radiation was a drawn-out event and major components such as diversity and abundance were discordant from each other. Crurotarsans (crocodile-line archosaurs) were more disparate, diverse, and abundant than avemetatarsalians (bird-line archosaurs, including dinosaurs) during the Late Triassic, but these roles were reversed in the Early Jurassic. There is no strong evidence that dinosaurs outcompeted or gradually eclipsed crurotarsans during the Late Triassic. Instead, crurotarsan diversity decreased precipitously by the end-Triassic extinction, which helped usher in the age of dinosaurian dominance.