This paper provides an introduction to Monte Carlo algorithms for pricing American options written on multiple assets, with special emphasis on methods that can be applied in a multi-dimensional setting. Simulated paths can be used to estimate by nonparametric regression the continuation value of the option or the optimal exercise policy and the value functions can then be computed by backward induction. The  exibility of nonparametric regression allows to obtain accurate price estimates with remarkable speed. For illustrative purpose we price oneand two-dimensional American options.