The authors present new techniques in the statistical methodology for selecting optimal subsets of features for data representation and classification. They provide guidelines for choosing an approach, depending on the extent of a priori knowledge of the problem. They review two basic approaches and specify the conditions for using those approaches. One approach involves computationally effective floating-search methods. The alternative approach trades off the requirement for a priori information for the requirement of sufficient data to represent the distributions involved. This approach is particularly suitable when the underlying probability distributions are not unimodal. It attempts to achieve simultaneous feature selection and decision-rule inference. According to the criterion adopted, this approach has two variants, allowing feature selection either for optimal representation or for discrimination.