We address the application of Monte Carlo simulation to the problem of pricing financial derivatives that allow early exercise opportunities. Up until 1993, it was commonly accepted in the finance community that simulation could not be applied to these American-style options. However, this belief has been all but refuted by a flurry of activity since then that has produced a number of simulation-based algorithms. We will briefly review the literature, and then present our approaches, which are based on converting the stochastic dynamic programming problem into a parametric optimization problem by characterizing the early exercise boundary. Stochastic approximation techniques are then applied to obtain a simulation-based algorithm. The related gradient estimation problem is addressed in this talk, and work in progress will also be described.