Graphs are used in many application domains to model entities and their relationships, such as social networks, the world-wide web, road maps, and communication networks. In a social network, for example, the entities are the users and their relationships are induced by their friendships in the social network. As a recent study showed, graphs modeling over a billion pair-wise relationships are ubiquitous. Additionally, many such graphs are not static, but are subject to a variety of changes. This leads to question how quickly information about a graph, for example which entities form clusters, can be updated when a change occurs. We will survey the state-of-the art of this research area on dynamic graph algorithms.