What is the role of unlabeled data in an inference problem, when the presumed underlying distribution is adversarially perturbed? In this talk, I explain how we answer to this question by unifying two major learning frame-works: Semi-Supervised Learning (SSL) and Distributionally Robust Optimization (DRO). We develop a generalization theory for our framework based on a number of novel complexity measures, such as an adversarial extension of Rademacher complexity and its semi-supervised analogue. Moreover, our analysis is able to quantify the role of unlabeled data in the generalization process under a more general condition compared to existing works in SSL. Based on our framework, we also present a hybrid of DRL and EM algorithms that has a guaranteed convergence rate. When implemented with deep neural networks, our method shows a comparable per-formance to those of the state-of-the-art on a number of real-world benchmark datasets.