Context: Process Debt, like Technical Debt, can be a source of short-term benefits but often is harmful in the long term for a software organization. Nonetheless, information about Process Debt is scarce in the current literature. Objective: This paper aims to define Process Debt, describe its occurrence with associated risks, and show examples of mitigation strategies. Method: Firstly, we conducted an exploratory study of Process Debt in four international organizations by interviewing 16 practitioners. Then, we validated and extended the findings with a cross-company focus group with additional 10 practitioners. Finally, we analyzed 58 additional observations and 35 interviews from a longitudinal case study. Results: The findings show that Process Debt can be a harmful phenomenon that needs attention. We provide a framework and a definition, and report causes, consequences and occurrence patterns over time of Process Debt. We present mitigation strategies and which ones need further attention for future research. Conclusions: The debt metaphor may help companies understand how to manage and improve their processes and make process-related decisions that are beneficial both in the short and long term.