Unmanned aerial vehicles are an emerging technology that can provide a superior option in obtaining remote data with less time, lower cost as well as higher safety compared to piloted aerial vehicles. Although promising, the performance of propulsion systems in unmanned aerial vehicles still needs to be significantly improved to meet the requirement for executing increasingly difficult missions. Due to the higher efficiency and better reliability comparing to conventional combustion engines, electrical systems with no greenhouse gas emission and low noise and vibration attract much more attention. Among them, fuel cells, as an advanced power generation technology, are regarded as alternative power sources in electrical systems because they offer higher energy density to extend the duration of flight. For the same energy capacity, the weight of fuel cells is 3.5 times lower than that of lithium-ion batteries, resulting in much preferable specific energy. This review article provides a general description of the working principle of fuel cells and the category of unmanned aerial vehicles, introduces two types of propulsion systems that involve fuel cells, i.e., pure fuel cell system and hybrid system, describes the design methods and simulation cases, as well as summarizes the practical flight tests.