Hydrogen is a promising energy carrier in all fields of transportation, including unmanned aerial vehicles (UAVs) and manned vehicles for urban air mobility (UAM). In these applications, one of the biggest challenges is to overcome the limitations of lithium battery technologies, while keeping the advantage of clean energy, at least in terms of direct emissions. For these reasons, there is an ever-increasing interest in the development, simulation, and testing of propulsion systems adopting air-cooled proton exchange membrane fuel cells (PEMFCs). Fuel cells for aerospace must be designed for power-to-weight maximization. For this reason, auxiliary systems are simplified, and the adoption of air-cooling and passive cooling techniques is favored. However, the performance and dynamic behavior of PEMFCs are affected by the operating conditions, which, in applications like UAVs and UAM, are continuously changing due to the variation of speed and altitude during the flight. This investigation analyzes semi-empirical and control-oriented models of fuel cell systems proposed in the scientific literature. The review addresses the whole fuel cell system, inclusive of the balance of the plant, and introduces the transition from dynamic models to digital twins.