In recent years, there has been an increasing demand for unmanned aerial vehicles (UAVs) with various capabilities suitable for both military and civilian applications. There is also a substantial interest in the development of novel drones that can fly autonomously in different environments and locations and perform various missions. Nevertheless, current battery-powered UAVs are limited by their flight range. Consequently, several approaches are being developed to enhance the flight endurance of drones, including augmenting the drone with solar power. In this review paper, we identify the different classifications of drones that have been developed based on their weight and flight range. Then, we explain the design challenges of the electrical systems embedded in the flying drones. Next, we discuss in detail approaches used to increase the flight endurance using various types of solar cells with respect to their materials and mechanical flexibility, in addition to various navigation and control approaches. Finally, limitations of existing solar-powered UAVs are presented in addition to proposed solutions and recommendations for the next generation of drones.