Geometric meshes consist of a set of points in 3D space connected in a (typically manifold) graph structure. As such they may be represented by a vector of 3n real values, where n is the number of vertices in the mesh. Unfortunately, although straightforward, this is not a very useful representation of the mesh, as it is difficult to naturally manipulate the mesh data using this representation. A better representation would capture the spatial correlation between vertices, be invariant to a class of natural transformations, not be too redundant, and be efficiently invertible. Recent years have seen the development of a variety of mesh representation schemes, intended primarily for mesh editing applications. In this talk I will survey some of these representation schemes, discuss their pros and cons, and demonstrate how they may be used to edit, animate and morph mesh datasets.