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Recent advances in quantum foundations have unveiled the idea that the causal order between quantum events may not always be fixed or even well-defined, allowing for some form of *indefinite quantum causality*. This tutorial will introduce the key concepts and motivations behind this rapidly developing area of research. Focusing on one of the main frameworks developed to explore indefinite quantum causality—the process matrix formalism—I will present key theoretical results, highlight the potential of indefinite causal orders as a resource for quantum information processing, and discuss experimental implementations as well as the physical interpretation of indefinite causal structures.