Unmanned Aerial Vehicle (UAV) propulsion technology is significantly related to the flight performance of UAVs, which has become one of the most important development directions of aviation. It should be noted that UAVs have three types of propulsion systems, namely the fuel, hybrid fuel-electric, and pure electric, respectively. This paper presents and discusses the classification, working principles, characteristics, and critical technologies of these three types of propulsion systems. It is helpful to establish the development framework of the UAV propulsion system and provide the essential information on electric propulsion UAVs. Additionally, future technologies and development, including the high-power density motors, converters, power supplies, are discussed for the electric propulsion UAVs. In the near future, the electric propulsion system would be widely used in UAVs. The high-power density system would become the development trend of electric UAVs. Thus, this review article provides comprehensive views and multiple comparisons of propulsion systems for UAVs.