Optimal transport(OT) provides a powerful and flexible way to compare, interpolate and morph probability measures. Originally proposed in the eighteenth century, this theory later led to Nobel Prizes for Koopmans and Kantorovich as well as C. Villani and A. Figalli Fields’ Medals in 2010 and 2018. OT is now used in challenging learning problems that involve high-dimensional data such as the inference of individual trajectories by looking at population snapshots in biology, the estimation of generative models for images, or more generally transport maps to transform samples in one space into another as in domain adaptation. With more than a hundred papers mentioning Wasserstein or transport in their title submitted at NeurIPS this year, and several dozens appearing every month acrossML/stats/imaging and data sciences, this workshop’s aim will be to federate and advancecurrent knowledge in this rapidly growing field.