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A computational problem in statistics concerns the reduction of the variance of an estimator of some quantity of interest. A typical example is rare event simulation, for which the standard deviation of most Monte Carlo estimators can be orders of magnitude larger than the quantity of interest. In this talk, I will explain how the development of variance reduction algorithms for rare events can benefit from exploiting variational principles from statistical mechanics in combination with techniques from stochastic optimal control. A particular focus will be on stochastic differential equations and rare events that involve unbounded random stopping times, which pose a particular challenge because the computational complexity of the rare event simulation also depends on average simulation time per sample that is not controlled by the variance. I will present recent results that reveal an unexpected connection between different rare event simulation algorithms and discuss further applications of statistical mechanics principles in computational stochastics.