One way of finding an "optimal" point configuration is to determine one that maximizes the sum of pairwise distances between distinct points. Specifically in the case of Euclidean distance on the sphere, such point sets are uniformly distributed, minimize the quadratic spherical cap discrepancy (which is equivalent to a certain worst case error estimate) over all point sets of the same cardinality. However, for other metrics on other spaces, such as geodesic distances on spheres or projective spaces, maximizing the sum of distances may not result in uniformly distributed point sets. We will discuss what is known in these settings, as well as recent progress in determining optimizers of the more general Geodesic Riesz energies on these spaces.