Due to the increasing integration of sustainability in corporate strategy, developing and implementing sustainable performance indicators in business processes is a growing focus of research and practice. This study aims to present the current state of research on sustainable business process performance measurement, considering the three dimensions of sustainability: environmental, social, and economic. This contribution identifies used sustainable metrics of business processes, evaluates their maturity, and outlines research gaps for future work. Conducting a systematic literature review results in a list of 72 sustainability performance indicators for business processes. The identified research focuses primarily on environmental indicators, while economic and social dimensions were mentioned less frequently. The maturity level of the sustainability metrics is rated as medium, as they are mostly only recorded but not consistently used, which indicates a lack of integration in practice. Thus, this study contributes to the existing literature by providing a comprehensive overview of the current state of research on performance metrics for sustainable business processes. This serves as a basis for future research, which should investigate methods for the long-term integration of such metrics in practice.