Due to the availability of more and more event data and mature process mining techniques, it has become possible to discover the actual processes within an organization. Process mining techniques use event logs to automatically construct process models that explain the behavior observed. Existing process models can be validated using conformance checking techniques. Moreover, the link between real-life events and model elements allows for the projection of additional information onto process models (e.g., showing bottlenecks and the flow of work within an organization). Although process mining has been mainly used within individual organizations, this new technology can also be applied in cross-organizational settings. In this paper, we identify such settings and highlight some of the challenges and opportunities. In particular, we show that cross-organizational processes can be partitioned along two orthogonal dimensions. This helps us to identify relevant process mining challenges involving multiple organizations.