When learning a mapping from an input space to an output space, the assumption that the sample distribution of the training data is the same as that of the test data is often violated. Unsupervised domain shift methods adapt the learned function in order to correct for this shift. Previous work has focused on utilizing unlabeled samples from the target distribution. We consider the complementary problem in which the unlabeled samples are given post mapping, i.e., we are given the outputs of the mapping of unknown samples from the shifted domain. Two other variants are also studied: the two sided version, in which unlabeled samples are give from both the input and the output spaces, and the Domain Transfer problem, which was recently formalized. In all cases, we derive generalization bounds that employ discrepancy terms. A Theory of Output-Side Unsupervised Domain Adaptation