Clustering is a classical unsupervised machine learning technique. It has various applications in criminal justice, automated resume processing, bank loan approvals, recommender systems and many more. Despite being so popular, traditional clustering algorithms may result in discriminatory behavior towards a group of people (or individuals) and have societal impacts. It has led to the study of fair clustering algorithms that aim to minimize the clustering cost while ensuring fairness. This chapter outlines existing group and individual fairness notions, discusses their relationships and comprehensively categorizes the current algorithms. The chapter further discusses the advantages and disadvantages of existing algorithms in terms of theoretical guarantees, time complexity and reproducibility. Finally, the chapter concludes with a discussion of new directions and open problems in the field of fair clustering. © The Institution of Engineers (India) 2023.