Hydrogen is emerging as a crucial energy source in the global effort to reduce dependence on fossil fuels and meet climate goals. Integrating hydrogen into Integrated Assessment Models (IAMs) is essential for understanding its potential and guiding policy decisions. These models simulate various energy scenarios, assess hydrogen’s impact on emissions, and evaluate its economic viability. However, uncertainties surrounding hydrogen technologies must be effectively addressed in their modeling. This review examines how different IAMs incorporate hydrogen technologies and their implications for decarbonization strategies and policy development, considering underlying uncertainties. We begin by analyzing the configuration of the hydrogen supply chain, focusing on production, logistics, distribution, and utilization. The modeling characteristics of hydrogen integration in 12 IAM families are explored, emphasizing hydrogen's growing significance in stringent climate mitigation scenarios. Results from the literature and the AR6 database reveal gaps in the modeling of the hydrogen supply chain, particularly in storage, transportation, and distribution. Model characteristics are critical in determining hydrogen’s share within the energy portfolio. Additionally, this study underscores the importance of addressing both parametric and structural uncertainties in IAMs, which are often underestimated, leading to varied outcomes regarding hydrogen's role in decarbonization strategies.