A growing number of clustering algorithms for categorical data have been proposed. This article describes the goals of clustering categorical data, such as scalability, robustness, and insensitivity to object ordering and minimal user‐specified parameters. We describe the main similarity metrics for categorical data, including Hamming distance and probabilistic metrics. We compare the different approaches to categorical data clustering, such as partition‐based, hierarchical, density‐based, and model‐based methods. We give examples of algorithms in each category and we explain what types of clustering goals each algorithm satisfies. We explain locality‐sensitive hashing as a fast similarity retrieval method for very large categorical datasets. We describe challenges for future work.