Chemical reaction data in journal articles, patents, and even electronic laboratory notebooks are currently stored in various formats, often unstructured, which presents a significant barrier to downstream applications, including the training of machine-learning models. We present the Open Reaction Database (ORD), an open-access schema and infrastructure for structuring and sharing organic reaction data, including a centralized data repository. The ORD schema supports conventional and emerging technologies, from benchtop reactions to automated high-throughput experiments and flow chemistry. The data, schema, supporting code, and web-based user interfaces are all publicly available on GitHub. Our vision is that a consistent data representation and infrastructure to support data sharing will enable downstream applications that will greatly improve the state of the art with respect to computer-aided synthesis planning, reaction prediction, and other predictive chemistry tasks.