Roughly speaking, clustering evolving networks aims at detecting structurally dense subgroups in networks that evolve over time. This implies that the subgroups we seek for also evolve, which results in many additional tasks compared to clustering static networks. We discuss these additional tasks and difficulties resulting thereof and present an overview on current approaches to solve these problems. We focus on clustering approaches in online scenarios, i.e., approaches that incrementally use structural information from previous time steps in order to incorporate temporal smoothness or to achieve low running time. Moreover, we describe a collection of real world networks and generators for synthetic data that are often used for evaluation.