Vector bundles of conformal blocks on M_{0,n} provide a collection of base point free divisors on M_{0,n} defined using representation theory. Specifically, from the data of a simple Lie algebra g, a nonnegative integer ell (called the level), and an n-tuple of dominant integral weights lambda, one can construct the bundle V(g, lambda, ell). The first Chern classes of nontrivial such bundles are base point free and so give rise to morphisms from M_{0,n} to other projective varieties. By studying the divisor classes, we can begin to classify the images of the induced maps.The main results of this dissertation concern combinatorial aspects of bundles defined using sL_r and sP_{2r}. We give identities between the divisors, study the cones they generate, and the associated morphisms. Our main tool involves a theorem known as Witten's Dictionary, which allows us to deploy methods of representation theory and combinatorics to analyze the behavior of vector bundles of conformal blocks.