Applications ranging from commercial entertainment to surgical training demand efficient methods for realistically modeling the appearance of physical phenomena in synthetic environments. In this talk, I will describe methods we have developed for simulating the behavior of a wide class of materials known as viscoelastic fluids and elastoplastic solids. These materials span a huge range of material properties including examples such as mucus, liquid soap, pudding, toothpaste, clay, wax, plastic, and steel. They exhibit a combination of both fluid and solid characteristics. Like a solid they can resist strain elastically, but under large or sustained strains they flow like a fluid. I'll talk about methods for modeling materials both at the predominantly fluid-like and predominantly solid-like ends of the spectrum. I will also briefly describe other simulation techniques for modeling phenomena such as explosions, fracture, real-time deformation, and even sound. One issue that arises recurrently is that all of these simulation techniques require clean geometric descriptions of the objects and environments they model. Unfortunately, most modeling techniques do not produce such clean descriptions. Even when clean models are available they often contain inappropriate amounts of detail. To address these issues I will show how highly detailed implicit surfaces can be built from defective input models using moving-leastsquares interpolation techniques.