Frege’s conception of axioms is an old-fashioned one. According to it, each axiom is a determinate non-linguistic proposition, one with a fixed subject-matter, and with respect to which the notion of a ‘model’ or an ‘interpretation’ makes no sense. As contrasted with the fruitful modern conception of mathematical axioms as collectively providing implicit definitions of structure-types, a conception on which the range of models of a set of axioms is of the essence of those axioms’ significance, Frege’s view is a dinosaur. This essay investigates some of the philosophically-important aspects of that dinosaur, in order to shed light on Frege’s understanding of the foundational role of axioms, and on some of the ways in which our current conception of such axiomatic virtues as independence and categoricity have (and in some cases have not) been informed by a move away from Frege’s understanding of the foundational role of axioms.