This chapter investigates subgroup discovery as a task of constraint-based mining of local patterns, aimed at describing groups of individuals with unusual distributional characteristics with respect to the property of interest. The chapter provides a novel interpretation of relevancy constraints and their use for feature filtering, introduces relevancy-based mechanisms for handling unknown values in the examples, and discusses the concept of relevancy as an approach to avoiding overfitting in subgroup discovery. The proposed approach to constraintbased subgroup mining, using the SD algorithm, was successfully applied to gene expression data analysis in functional genomics.