  Recently, Optimal Transport has been proposed as a probabilistic framework in
Machine Learning for comparing and manipulating probability distributions. This
is rooted in its rich history and theory, and has offered new solutions to
different problems in machine learning, such as generative modeling and
transfer learning. In this survey we explore contributions of Optimal Transport
for Machine Learning over the period 2012 -- 2022, focusing on four sub-fields
of Machine Learning: supervised, unsupervised, transfer and reinforcement
learning. We further highlight the recent development in computational Optimal
Transport, and its interplay with Machine Learning practice.
