Maria Emelianenko George Mason University Many technologically important properties of polycrystalline materials are affected by the mesoscopic features of their microstructure, such as average sizes of the grains as well as lengths and types of interfaces between them. This lecture will focus on mathematical modeling approaches related to crystal grain growth and will include numerical demonstrations as well as a short survey of recent developments in this area. Particular attention will be paid to curvature driven growth modeling and simulation techniques and mathematical theories describing coarsening rates and evolution of grain boundary statistics.