Logistics and production systems are confronted with a highly volatile business environment, a situation which increasingly pushes common supply chain analytics approaches to their limits. Process mining is an emerging technique to provide insights into business processes as they are being executed. However, the application of process mining in cross-organizational context has not been conclusively researched. In a literature overview, we review a set of 34 papers on the application of process mining in supply chains and classify them according to a three-stage maturity model. We find the majority of academic publications (28 papers) to focus on the construction of cross-organizational process models, 5 publications to derive models for alerting deviations and recommending decision support, and 1 paper to focus on automatic adjustments of the system behavior. Based on these findings, we conclude that the exploitation of process mining will be a key competitive advantage in supply chain management in the upcoming years. This applies not only for the design and management of steady-state supply chains, but also for the rapid adaptation of new solutions in transient systems.