This study is an interpretation of Descartes' theory of space and vacuum. Descartes famously holds that space is identical to matter, and that a vacuum or empty space is logically impossible. These positions earned Descartes a great deal of criticism from philosophers during the seventeenth and eighteenth centuries. Two main strands of criticism are dealt with here. First, Descartes was charged with dogmatism for holding that rival notions of space were inconceivable, a position for which he seems to have no good arguments. Second, some philosophers claimed that Descartes is guilty of inconsistency: his position on the vacuum, they said, was incompatible with his theory of the metaphysics of extended substance. This dissertation comprises a comprehensive interpretation of Descartes' treatment of space and vacuum, particularly in the Principles of Philosophy (1644). A new reading of the discussion of place and space in Principles Part II is articulated and defended; the result is a fundamental rethinking of what Descartes means by the claim that body and space are identical. This reinterpretation provides the basis for the culminating point of the study. Descartes' position on the vacuum is discussed in relation to a number of different understandings of what a vacuum might be. The different arguments he offers concerning the vacuum are analyzed and related to each other. Two chapters are devoted to objections raised by Arnauld, Henry More, and Spinoza. The implications of these objections for Descartes' theory of extended substance are pursued in these chapters, and direction for further research on this topic is discussed in an appendix. The central thesis argued here is that Descartes' position on space and vacuum is more plausible in its context than has been recognized. It turns out that Descartes takes great care to address the strengths of his opponents' positions on space and vacuum, and that he has an argument for his view involving an appeal to ontological economy or simplicity. His position on this topic, which is commonly taken to be a paradigmatic example of dogmatism, is argued for more plausibly, and more responsibly, than has previously been recognized.