Machine Learning (ML) is an expressive framework for turning data into computer programs. Across many problem domains---both in industry and policy settings—the types of computer programs needed for accurate prediction or optimal control are difficult to write by hand. On the other hand, collecting instances of desired system behavior may be relatively more feasible. This makes ML broadly appealing, but also induces data sensitivities that often manifest as unexpected failure modes during deployment. In this sense, the training data available tend to be imperfect for the task at hand. This thesis explores several data sensitivities of modern machine learning and how to address them. We begin by discussing how to prevent ML from codifying prior human discrimination measured in the training data, where we take a fair representation learning approach. We then discuss the problem of learning from data containing spurious features, which provide predictive fidelity during training but are unreliable upon deployment. Here we observe that insofar as standard training methods tend to learn such features, this propensity can be leveraged to search for partitions of training data that expose this inconsistency, ultimately promoting learning algorithms invariant to spurious features. Finally, we turn our attention to reinforcement learning from data with insufficient coverage over all possible states and actions. To address the coverage issue, we discuss how causal priors can be used to model the single-step dynamics of the setting where data are collected. This enables a new type of data augmentation where observed trajectories are stitched together to produce new but plausible counterfactual trajectories.