Major domains such as logistics, healthcare, and smart cities increasingly rely on sensor technologies and distributed infrastructures to monitor complex processes in real time. These developments are transforming the data landscape from discrete, structured records stored in centralized systems to continuous, fine-grained, and heterogeneous event streams collected across distributed environments. As a result, traditional process mining techniques, which assume centralized event logs from enterprise systems, are no longer sufficient. In this paper, we discuss the conceptual and methodological foundations for this emerging field. We identify three key shifts: from offline to online analysis, from centralized to distributed computing, and from event logs to sensor data. These shifts challenge traditional assumptions about process data and call for new approaches that integrate infrastructure, data, and user perspectives. To this end, we define a research agenda that addresses six interconnected fields, each spanning multiple system dimensions. We advocate a principled methodology grounded in algorithm engineering, combining formal modeling with empirical evaluation. This approach enables the development of scalable, privacy-aware, and user-centric process mining techniques suitable for distributed environments. Our synthesis provides a roadmap for advancing process mining beyond its classical setting, toward a more responsive and decentralized paradigm of process intelligence.