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The use of mathematical modeling for the purpose of analyzing and optimizing the performance of repairable systems is widely studied in the literature. In this dissertation, we study two different scenarios on the maintenance modeling and optimization of repairable systems. First, we study the long-run availability of a traditional repairable system that is subjected to imperfect corrective maintenance. We use Kijima's second virtual age model to describe the imperfect repair process. Because of the complexity of the underlying probability models, we use simulation modeling to estimate availability performance and meta-modeling to convert the reliability and maintainability parameters of the repairable system into an availability estimate without the simulation effort. As a last step, we add age-based, perfect preventive maintenance to our analysis. Second, we optimize a preventive maintenance policy for a two-component repairable system. When either component fails, instantaneous, minimal, and costly corrective maintenance is performed on the component. At equally-spaced, discrete points during the system's useful life, the decision-maker has the option to perform instantaneous, imperfect, and costly preventive maintenance on one or both of the components, to instantaneously replace one or both of the components, or to do nothing. We use a Genetic Algorithm in an attempt to find a cost-optimal set of preventive maintenance and replacement decisions.