Particulate systems have proven difficult to probe experimentally in many instances. Simulations of granular flows, and mixing flows in particular. provide a useful means of studying particulate behavior. Mixing flows generate large scale patterns and structures which can be easily visualized. Thus, mixing studies provide a means of indirectly examining granular flows. In this paper we review recent computational studies of tumbler mixing, focusing on two very different, yet complementary, techniques: Particle Dynamics and Lagrangian Simulation. We discuss mixing in different tumbler geometries, as well as segregation and cohesive effects.