At the end of the 18th century, Gaspard Monge introduced the optimal transport problem to understand the most efficient way of transporting a distribution of material from one place to another to build fortifications. In the last 30 years, this theory has found various applications in many areas of mathematics. However, more recently, optimal transport has also become a very powerful tool in many areas of machine learning. In this talk, we will give an overview of optimal transport, with some selected applications.