Networks allow the representation of interactions between objects. Their structures are often complex to explore and need some algorithmic and statistical tools for summarizing. One possible way to go is to cluster their vertices into groups having similar connectivity patterns. This chapter aims at presenting an overview of clustering methods for network vertices. Common community structure searching algorithms are detailed. The well-known Stochastic Block Model (SBM) is then introduced and its generalization to overlapping mixed membership structure closes the chapter. Examples of application are also presented and the main hypothesis underlying the presented algorithms discussed.