The simultaneous perturbation stochastic approximation (SPSA) algorithm is an established method for solving multivariate optimization problems arising in stochastic systems. The essential feature of SPSA, which accounts for its power and relative ease of use in challenging problems, is the underlying gradient approximation that requires only two objective function measurements regardless of the dimension of the optimization problem. This talk will be a blend of discussion about the basic ideas behind SPSA and some recent advances in areas such as discrete optimization and adaptive (second-order) methods.