Data clustering is a popular unsupervised data mining tool that is used for partitioning a given dataset into homogeneous groups based on some similarity/dissimilarity metric. Traditional clustering algorithms often make prior assumptions about the cluster structure and adopt a corresponding suitable objective function that is optimized either through classical techniques or metaheuristic approaches. These algorithms are known to perform poorly when the cluster assumptions do not hold in the data. Multiobjective clustering, in which multiple objective functions are simultaneously optimized, has emerged as an attractive and robust alternative in such situations. In particular, application of multiobjective evolutionary algorithms for clustering has become popular in the past decade because of their population-based nature. Here, we provide a comprehensive and critical survey of the multitude of multiobjective evolutionary clustering techniques existing in the literature. The techniques are classified according to the encoding strategies adopted, objective functions, evolutionary operators, strategy for maintaining nondominated solutions, and the method of selection of the final solution. The pros and cons of the different approaches are mentioned. Finally, we have discussed some real-life applications of multiobjective clustering in the domains of image segmentation, bioinformatics, web mining, and so forth.