Hyperbolic geometric structures on manifolds are a very well-studied area of geometry and topology, but these are "just" a subset of a larger class of geometric structures known as convex projective structures. These are geometric structures that are locally modeled on RPn with transition maps in PGL(n+1,R), the group of projective transformations. We will begin with the story for convex projective surfaces which were studied by Goldman and shown to have a beautiful deformation theory, and then segue to the work of Benoist which takes on the higher dimensional cases and shows that these too admit a rich deformation theory. Even more, Benoist gives an elegant characterization of discrete subgroups preserving a proper convex domain which boils down to simply knowing whether or not there are line segments in the boundary.