Monte Carlo is a computational workhorse for valuation of financial securities and risk. It is directly applicable to almost all types of financial securities and is robust in that it is insensitive to the complexities of a security. On the other hand, Monte Carlo can be terribly slow and inaccurate. This talk will review the basics of Monte Carlo quadrature in the context of finance and methods for its acceleration, including variance reduction, quasi-Monte Carlo and ad hoc methods. American options, for which the exercise time is chosen by the option holder, are a class of securities to which Monte Carlo is not directly applicable. The talk will also describe the recently developed Least Square Monte Carlo (LSM) method for American options, some generalizations of LSM, and methods for estimating the accuracy of Monte Carlo for American options.