Cliques and graph theoretic clique relaxations are used to model clusters in graph-based data mining, where data is modeled by a graph in which an edge implies some relationship between the entities represented by its endpoints. The need for relaxations of the clique model arises in practice when dealing with massive data sets which are error-prone, resulting in false or missing edges. The clique definition which requires complete pairwise adjacency in the cluster becomes overly restrictive in such situations. Graph theoretic clique relaxations address this need by relaxing structural properties of a clique in a controlled manner via user-specified parameters. This chapter surveys such clique relaxations available in the literature primarily focussing on polyhedral results, complexity studies, approximability, and exact algorithmic approaches.