This chapter is a first introduction to optimal vector quantization and its application to numerical probability. Optimal quantization produces the best approximation of probability distribution by finitely supported distributions in the sues of the Wasserstein distance. It naturally yields cubature formulas to compute. An appropriate Richardson–Romberg extrapolation based on the combination of such cubature formulas turn out to be competitive with regular Monte Carlo simulation up to at least 5 dimensions. A first approach to the computation of (quadratic) optimal quantizers of a given distribution is developed. Quantization is also investigated in chapter 6 from an algorithmic view point and 11 as a numerical method to price American and Bermudan options.