Clustering is a fundamental problem in unsupervised machine learning. The goal of this problem is to partition a set of given data points so that similar points are grouped together. In this talk, I’ll give an overview of several ways to formalize this problem and algorithms that have been proposed to solve them. Many applications of clustering require the solution to satisfy additional desirable properties such as fairness. I will give a formal definition of clustering with fairness, and present a number of recent results in this area.