Optimal transport (OT) is gradually establishing itself as a powerful and essential tool to compare probability measures, which in machine learning take the form of point clouds, histograms, bags-of-features, or more generally datasets to be compared with probability densities and generative models. OT can be traced back to early work by Monge, and later to Kantorovich and Dantzig during the birth of linear programming. The mathematical theory of OT has produced several important developments since the 90's, crowned by Cédric Villani's Fields Medal in 2010. OT is now transitioning into more applied spheres, including recent applications to machine learning, because it can tackle challenging learning scenarios including dimensionality reduction, structured prediction problems that involve histograms, and estimation of generative models in highly degenerate, high-dimensional problems. This workshop will follow that organized 3 years ago (NIPS 2014) and will seek to amplify that trend. We will provide the audience with an update on all of the very recent successes brought forward by efficient solvers and innovative applications through a long list of invited talks. We will add to that a few contributed presentations (oral, and, if needed posters) and, finally, a panel for all invited speakers to take questions from the audience and formulate more nuanced opinions on this nascent field.