We consider the problem of learning to repair programs from diagnostic feedback (e.g., compiler errors). Program repair is challenging for two reasons: First, it requires reasoning and tracking symbols across the source code and diagnostic messages. Second, labeled datasets available for program repair are limited in size. This work proposes novel solutions to those two challenges. First, we introduce a program-feedback graph, which connects symbols relevant to error fixing in source code and diagnostic messages, and then apply a graph-attentional network on top to model the reasoning process. Second, we present a self-supervised learning paradigm for program repair that leverages unlabeled program data available online to create a large amount of extra program repair examples, which we use to pre-train our models. We evaluate our proposed approach on two applications: correcting introductory programming assignments (DeepFix dataset) and correcting the outputs of program synthesis (SPoC dataset). Our final system, DrRepair, significantly outperforms prior work, achieving state-of-the-art results on both tasks: 66