Process automation has been a cornerstone of business process management, enabling organizations to streamline operations through predefined rules and procedures. However, a new paradigm is emerging: process autonomization. It has the potential to disrupt the core of business process management and the methods and tools that have characterized it for the last century. This paper introduces and conceptualizes process autonomization as distinct from traditional automation, characterized by the key capabilities of artificial autonomy: independence, neglect tolerance, and indeterminism. We demonstrate how autonomization transcends predefined machine behaviors to handle tasks that have traditionally required human involvement. Further, we identify three critical aspects for process autonomization: explicit goal specification, macro-level resource allocation, and appropriate constraint definition. We discuss them across the process lifecycle stages of build time, run time, and change time. Our analysis also reveals that process autonomization introduces new reliability and explainability caveats. We contribute to theory by providing a conceptual framework for understanding process autonomization and offer practical insights for organizations considering the transition from automated to autonomized processes.