Clustering is the unsupervised method of grouping data samples to form a partition of a given dataset. Such grouping is typically done based on homogeneity assumptions of clusters over an attribute space and hence the precise definition of the similarity metric affects the clusters inferred. In recent years, new formulations of clustering have emerged that posit indirect constraints on clustering, typically in terms of preserving dependencies between data samples and auxiliary variables. These formulations find applications in bioinformatics, web mining, social network analysis, and many other domains. The purpose of this survey is to provide a gentle introduction to these formulations, their mathematical assumptions, and the contexts under which they are applicable.