This talk reports on recent work in what has been called ``Mac Lane set theory'', a categorical set theory with a global membership relation among the objects. In contrast to elementary topos theory, such categories of sets model elementary set theory directly. We use the methods developed by Joyal and Moerdijk, employing an axiomatic notion of a system of small maps in a category of classes, which serve to limit comprehension in a new and flexible way. We show that *every* elementary topos arises as such a category of sets, and that (a certain) elementary set theory is deductively complete with respect to such topos models. An further new result in this connection is that the axiom scheme of full Replacement is conservative over bounded intuitionistic Zermelo set theory.