Simulation of natural phenomena for virtual worlds and characters is an important aspect of computer graphics that remains extremely challenging. By modeling the complex motion of phenomena such as breaking ocean waves, crumbling sand castles and falling snow, computer graphics researchers can create realistic virtual environments for a wide range of applications. The most challenging natural phenomena are those whose dynamics involve dramatic topological changes and therefore require sophisticated numerical approaches to achieve sufficient accuracy and visual realism. The need for computational efficiency, topological variability, and numerical stability has led my research toward hybrid, Lagrangian/Eulerian methods, particularly the Material Point Method (MPM). In this talk, I will focus on my recent research on elastoplasticity and multi-physics simulation with MPM for computer graphics applications and other related engineering fields.