  This chapter describes techniques for the numerical resolution of optimal
transport problems. We will consider several discretizations of these problems,
and we will put a strong focus on the mathematical analysis of the algorithms
to solve the discretized problems. We will describe in detail the following
discretizations and corresponding algorithms: the assignment problem and
Bertsekas auction's algorithm; the entropic regularization and Sinkhorn-Knopp's
algorithm; semi-discrete optimal transport and Oliker-Prussner or damped
Newton's algorithm, and finally semi-discrete entropic regularization. Our
presentation highlights the similarity between these algorithms and their
connection with the theory of Kantorovich duality.
