According to string theory, we may live in a world with more than three spatial dimensions. The traditional approach to obtaining large four dimensional universes from theories with more than four space-time dimensions is to assume that the extra dimensions are tightly curled up or "compactified" into a tiny space. In this talk we will explore the geography of this space. In particular, we shall see how the detailed properties of the four dimensional physics are determined by the properties of this tiny space. Avoiding complex mathematical details, I will review recent progress in understanding compactifications on special holonomy manifolds which provide elegant models of supersymmetric particle physics and gravity. I will also discuss a new class of models, called "flux compactifications", which has recently attracted considerable attention. These models play an important role in exploring the space of string vacua and provide a natural solution to the moduli problem, one of the central problems in superstring phenomenology.