The interest in electric unmanned aerial vehicles (UAVs) is rapidly growing in recent years. The reason is that UAVs have abilities to perform some difficult or dangerous tasks, with high mobility, safety, and low cost. It should be noted that UAVs are revolutionizing many public services including real time monitoring, search and rescue, wildlife surveys, delivery services, wireless coverage, and precision agriculture. To increase endurance and achieve good performance, UAVs generally use a hybrid power supply system architecture. A hybrid power architecture may combine several power sources such as fuel cell, battery, solar cells, and supercapacitor. The choice of a suitable power source hybridization architecture with an optimal energy management system are therefore crucial to enable an efficient operation of advanced UAVs. In the context of battery-powered UAV platforms, including new technologies such as swapping laser-beam inflight recharging and tethering, this paper proposes a comprehensive and critical state of the art review on power supply configurations and energy management systems to find out gaps and to provide insights and recommendations for future research.