Reading comprehension has recently seen rapid progress, with systems matching humans on the most popular datasets for the task. However, a large body of work has highlighted the brittleness of these systems, showing that there is much work left to be done. We introduce a new reading comprehension benchmark, DROP, which requires Discrete Reasoning Over the content of Paragraphs. In this crowdsourced, adversarially-created, 55k-question benchmark, a system must resolve references in a question, perhaps to multiple input positions, and perform discrete operations over them (such as addition, counting, or sorting). These operations require a much more comprehensive understanding of the content of paragraphs, as they remove the paraphrase-and-entity-typing shortcuts available in prior datasets. We apply state-of-the-art methods from both the reading comprehension and semantic parsing literatures on this dataset and show that the best systems only achieve 38.4% F1 on our generalized accuracy metric, while expert human performance is 96%. We additionally present a new model that combines reading comprehension methods with simple numerical reasoning to achieve 51% F1.