Artificial intelligence (AI) has emerged as one of the most formative technologies of the century and further gains importance to solve the big societal challenges (e.g. achievement of the sustainable development goals) or as a means to stay competitive in today’s global markets. The role as a key enabler in many areas of our daily life leads to a growing dependence, which has to be managed accordingly to mitigate negative economic, societal or privacy impacts. Therefore, the European Union is working on an AI Act, which defines concrete governance, risk and compliance (GRC) requirements. One of the key demands of this regulation is the operation of a risk management system for High-Risk AI systems. In this paper, we therefore present a detailed analysis of relevant literature in this domain and introduce our proposed approach for an AI Risk Management System (AIRMan).