Everyone knows what David Lewis' possible worlds are, what role they play in his account of possibility and necessity, and Saul Kripke's criticisms. But what, instead, are Kripke's possible worlds, and what role do they play in his account of possibility and necessity? The answers are not so obvious. Recently, it has even been claimed that, contrary to what is standardly assumed, Kripke's approach to modality has not always been consistently metaphysical. In particular, an interpretation of the famous passage in (...) the preface to Naming and Necessity with Kripke's discussion of the dice example has been put forward, according to which he purports there to clarify the modal notions in terms of that of possible world, model-theoretically construed, in a way which is reminiscent of Carnap's. In this paper, I shall point out some internal difficulties of this interpretation, and offer a different one, according to which in the dice passage Kripke is trying, consistently with his metaphysical approach, to legitimize the technically useful notion of possible world starting from modal notions, to be accounted for in another way (arguably, in an essentialistic framework). My final goal, however, will be philosophical elucidation rather than mere exegesis. Indeed, I am interested in shedding some light on what possible worlds might possibly be, if something like Kripke's metaphysical approach is on the right track. (shrink)