Optimization-based decision support systems have a significant potential to reduce delays, and thus improve efficiency on the railways, by automatically re-routing and re-scheduling trains after delays have occurred. The operations research community has dedicated a lot of effort to developing optimization algorithms for this problem, but each study is typically tightly connected with a specific industrial use case. Code and data are seldom shared publicly. This fact hinders reproducibility, and has led to a proliferation of papers describing algorithms for more or less compatible problem definitions, without any real opportunity for readers to assess their relative performance. Inspired by the successful communities around MILP, SAT, TSP, VRP, etc., we introduce a common problem definition and file format, DISPLIB, which captures all the main features of train re-routing and re-scheduling. We have gathered problem instances from multiple real-world use cases and made them openly available. In this paper, we describe the problem definition, the industrial instances, and a reference solver implementation. This allows any researcher or developer to work on the train dispatching problem without an industrial connection, and enables the research community to perform empirical comparisons between solvers. All materials are available online at https://displib.github.io.