This chapter discusses the role of multivariate design of experiments (DOE) and optimization through the multivariate approach. DOE and optimization of processes through the well-known response surface methodology are issues of paramount importance in real world applications considering that its implementation consumes less time and requires fewer efforts and resources than the use of univariate procedures for the same purpose. Several designs are available for implementation when the objective is to model a second order response surface. The chapter provides a brief descriptions of four most commonly used designs in published reports: full factorial, central composite, Box-Behnken, and mixture simplex centroid designs. The number of factors to be considered can be important, it is necessary to perform screening experiments to determine the experimental variables and interactions that have a significant influence on one or several response. The artificial neural networks methodology was especially created to model nonlinear information, simulating some properties of the human brain.