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Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential equation approach by generating typical system histories, instead of just statistical measures such as the mean and variance of a population. Simple simulations are now easy for students to construct from scratch—that is, without recourse to black-box packages. In some cases, their results can also be compared directly with single-molecule experimental data. After introducing the stochastic simulation algorithm, this article gives two case studies involving gene expression and error correction, respectively. For gene expression, stochastic simulation results are compared with experimental data, an important research exercise for biophysics students. For error correction, several proofreading models are compared to find the minimal components necessary for sufficient accuracy in translation. Animations of the stochastic error correction models provide insight into the proofreading mechanisms. Code samples and resulting animations showing results are given in the online Supplemental Material .