Recent advances in process mining technology have extended its applicability beyond traditional domains such as healthcare, finance and manufacturing, making it increasingly relevant for addressing problems in supply chain management. In our research, we explore the integration of process mining techniques within the domain of supply chain management, focusing on uncovering inefficiencies, ensuring compliance, and identifying opportunities for improvement. Therefore, we first review the technological advances in process mining relevant to supply chain management and outline six relevant approaches. We then combine the identified methodologies with expert interviews to derive and validate six specific use cases where process mining can significantly contribute to supply chain efficiency and resilience. The paper presents a detailed description of these use cases, demonstrating how process mining can provide actionable insights for a wide range of supply chain problems. We discuss the implications of our findings for practitioners, who benefit from enhanced visibility and optimisation opportunities, and researchers, who are provided with a roadmap for exploration of this promising interdisciplinary field. To the best of our knowledge, this is the first work to explore potential use cases for process mining in a supply chain context, providing a comprehensive perspective on the potential benefits and challenges.