This talk describes a practical algorithm based on Monte Carlo simulation for the pricing of multi-dimensional American (i.e., continuously exercisable) and Bermudan (i.e., discretely-exercisable) options. The method generates both lower and upper bounds for the option price and hence gives valid confidence intervals for the true value. Lower bounds can be generated using any number of primal algorithms. Upper bounds are generated using a new Monte Carlo algorithm based on a duality representation of the Bermudan value function. Computational results for multi-factor equity and interest rate options demonstrate the simplicity and efficiency of the proposed algorithm.