Optimal transport is a theory at the intersection of optimization, partial differential equations, and probability. Given two probability measures, optimal transport consists in finding the best way to transform the first into the second. It has recently emerged as a powerful tool for addressing a surprisingly wide range of applied problems, particularly in machine learning. In this talk, I will introduce the main concepts of optimal transport, from Monge’s problem to Kantorovich’s formulation and we will look at several application examples. We will eventually study the case of the analysis of flow cytometry data in the context of acute myeloid leukemia—an area where the use of optimal transport is still limited due to its high computational cost.