This working paper is a review of adaptations of the Monte Carlo simulation methodology to American options valuation. In examining this topic, we discuss why other numerical methods, such as multinomial lattice and finite-difference methodologies, are often inadequate for the valuation of complex American options. We then describe three classes of adaptations of the Monte Carlo simulation approach for American options pricing -- the regression-based method, the stochastic mesh method, and state-space partitioning method -- which are designed to address the deficiencies of other numerical methods in pricing American options. As part of our survey, we contrast these three approaches.