Parallel computers have been very effective tools in the study of cosmological structure formation and our understanding of the dynamical evolution of the Universe. The simulations use particles which represent packets of the phase fluid which for dark matter behaves as an incompressible fluid in the 6-dimensional phase space. Accuracy of such simulations is primarily dictated by the number of particles used since the methods are based on Monte-Carlo integration. As more particles are used the densities that can be resolved in the simulations increases. This greatly increases the difficulties associated with load balancing on a parallel computer and current simulations set an ever increasing challenge to scaling on parallel architectures. I will discuss these problems and some of the strategies used to alleviate them. New machines with up to 1 million processors seem to require a new approach and I will discuss ways in which one can achieve efficiency at even this scale of parallelism.