The richness of definitions and features of the community-detection problem has led to an impressive body of literature. In fact, many community-detection methods and surveys have been introduced in recent years. The goal here is to present a state-of-the-art of the most mature research in this area. We will therefore concentrate on non-overlapping community detection with the basic graph model. In this chapter we will give an overview of the most influential approaches to community detection that encompass most of the main methods and techniques. A special focus will also be given to community evaluation.