Many of the modern techniques to solve supervised learning problems suffer from a lack of interpretability and analyzability that do not give rise to rigorous mathematical results. This monograph develops a comprehensive statistical learning framework that uses Distributionally Robust Optimization (DRO) under the Wasserstein metric to ensure robustness to perturbations in the data. The authors introduce the reader to the fundamental properties of the Wasserstein metric and the DRO formulation, before explaining the theory in detail and its application. They cover a series of learning problems, including (i) distributionally robust linear regression; (ii) distributionally robust regression with group structure in the predictors; (iii) distributionally robust multi-output regression and multiclass classification; (iv) optimal decision making that combines distributionally robust regression with nearest-neighbor estimation; (v) distributionally robust semi-supervised learning; (vi) distributionally robust reinforcement learning. Throughout the monograph, the authors use applications in medicine and health care to illustrate the theoretical ideas in practice. They include numerical experiments and case studies using synthetic and real data. Distributionally Robust Learning provides a detailed insight into a technique that has gained a lot of recent interest in developing robust supervised learning solutions that are founded in sound mathematical principles. It will be enlightening for researchers, practitioners and students working on the optimization of machine learning systems.