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This article presents a basic introduction and some advanced concepts used in the use of cellular automata for the modeling and simulation of the motion of grain boundaries in evolving microstructures. An attempt is made to compile a complete review of literature in this context only. It is illustrated how cellular automata can be used to describe grain boundary motion when driven by the minimization of volume-stored energy as well as when it is curvature driven. Attention is drawn to the typical problems that may occur when modeling grain boundary surface topologies using discretized numerical representations, and extended information is given on a previously published solution to this problem with irregular cellular automata. Finally, an example of a hybrid model is given, combining cellular automata with a computational description of diffusion and precipitate dissolution with an application to the problem of abnormal grain growth.