This dissertation is a defense of a particular theory of the metaphysics of time which I call "accretivism", but which is popularly known in a form usually called the "Growing Block Theory". The goal of a metaphysics of time is to incorporate the various aspects of our temporal experience into a single, comprehensive whole. To this end I delineate five aspects of our ordinary experience of time: 1) The Tensed Aspect, in virtue of which objects are presented to us as (...) past, present, or future; 2) The Transitory Aspect, in virtue of which time passes or "flows"; 3) The Durational Aspect, in virtue of which entities have a certain temporal extent; 4) The Structural Aspect, in virtue of which entities are given as being in temporal relations to one another, and 5) The Differential-Repetitive Aspect, in virtue of which things are different from one time to another, and yet there is a certain recurrence of aspects of our experience form one time to another. I contrast the accretivist picture of time, according to which that which is past and that which is present both have ontological status, but nothing which is future has ontological status, and in which temporal passage consists in the coming-into-being of new entities at the temporal edge of reality marked by the present, with the two dominant theories of time in the contemporary literature: 1) presentism, according to which only that which is present has ontological status, and 2) four-dimensionalism, according to which time is to be understood on analogy with spatial dimensions. Accretivism, I argue, is superior to the other two views in virtue of the fact that it gives full status to both the Structural Aspect of Time, for which the presentist has difficulty accounting, and the Transitory Aspect of Time, for which the four-dimensionalist has difficulty accounting. I then defend the accretivist picture against a variety of objections that might be raised to it. (shrink)