The assignment of alternatives (observations/objects) into predefined homogenous groups is a problem of major practical and research interest. This type of problem is referred to as classification or sorting, depending on whether the groups are nominal or ordinal. Methodologies for addressing classification and sorting problems have been developed from a variety of research disciplines, including statistics/econometrics, artificial intelligent and operations research. The objective of this paper is to review the research conducted on the framework of the multicriteria decision aiding (MCDA). The review covers different forms of MCDA classification/sorting models, different aspects of the model development process, as well as real-world applications of MCDA classification/sorting techniques and their software implementations.