This paper describes fundamentals and applications of multivariate statistical techniques for the optimization of chromatographic systems. The surface response methodologies: central composite design, Doehlert matrix and Box-Behnken design are discussed and applications of these techniques for optimization of sample preparation steps (extractions) and determination of experimental conditions for chromatographic separations are presented. The use of mixture design for optimization of mobile phases is also related. An optimization example involving a real separation process is exhaustively described. A discussion about model validation is presented. Some applications of other multivariate techniques for optimization of chromatographic methods are also summarized.