Domain adaptation enables knowledge transfer from a labeled source domain to an unlabeled target domain. A mainstream approach is adversarial feature adaptation, which learns domain-invariant representations through aligning the feature distributions of both domains. However, a theoretical prerequisite of domain adaptation is the adaptability measured by the expected risk of an ideal joint hypothesis over the source and target domains. In this respect, adversarial feature adaptation may potentially deteriorate the adaptability, since it distorts the original feature distributions when suppressing domain-specific variations. To this end, we propose Transferable Adversarial Training (TAT) to enable the adaptation of deep classifiers. The approach generates transferable examples to fill in the gap between the source and target domains, and adversarially trains the deep classifiers to make consistent predictions over the transferable examples. Without learning domain-invariant representations at the expense of distorting the feature distributions, the adaptability in the theoretical learning bound is algorithmically guaranteed. A series of experiments validate that our approach advances the state of the arts on a variety of domain adaptation tasks in vision and NLP, including object recognition, learning from synthetic to real data, and sentiment classification.