We present SParC, a dataset for cross-domain Semantic Parsing in Context. It consists of 4,298 coherent question sequences (12k+ individual questions annotated with SQL queries), obtained from controlled user interactions with 200 complex databases over 138 domains. We provide an in-depth analysis of SParC and show that it introduces new challenges compared to existing datasets. SParC (1) demonstrates complex contextual dependencies, (2) has greater semantic diversity, and (3) requires generalization to new domains due to its cross-domain nature and the unseen databases at test time. We experiment with two state-of-the-art text-to-SQL models adapted to the context-dependent, cross-domain setup. The best model obtains an exact set match accuracy of 20.2% over all questions and less than 10% over all interaction sequences, indicating that the cross-domain setting and the contextual phenomena of the dataset present significant challenges for future research. The dataset, baselines, and leaderboard are released at https://yale-lily.github.io/sparc.