We study the task of semantic parse correction with natural language\nfeedback. Given a natural language utterance, most semantic parsing systems\npose the problem as one-shot translation where the utterance is mapped to a\ncorresponding logical form. In this paper, we investigate a more interactive\nscenario where humans can further interact with the system by providing\nfree-form natural language feedback to correct the system when it generates an\ninaccurate interpretation of an initial utterance. We focus on natural language\nto SQL systems and construct, SPLASH, a dataset of utterances, incorrect SQL\ninterpretations and the corresponding natural language feedback. We compare\nvarious reference models for the correction task and show that incorporating\nsuch a rich form of feedback can significantly improve the overall semantic\nparsing accuracy while retaining the flexibility of natural language\ninteraction. While we estimated human correction accuracy is 81.5%, our best\nmodel achieves only 25.1%, which leaves a large gap for improvement in future\nresearch. SPLASH is publicly available at https://aka.ms/Splash_dataset.\n