Community discovery is one of the most studied problems in network science. In recent years, many works have focused on discovering communities in temporal networks, thus identifying dynamic communities. Interestingly, dynamic communities are not mere sequences of static ones; new challenges arise from their dynamic nature. In this chapter, we will discuss some of these challenges and recent propositions to tackle them. We will, among other topics, discuss on the question of community events in gradually evolving networks, on the notion of identity through change, on dynamic communities in link streams, on the smoothness of dynamic communities, and on the different types of complexity of algorithms for their discovery.