This study is conducted in the context of two significant challenges facing Unmanned Aerial Vehicle (UAV) technologies. These challenges are limited flight duration and payload, which have a direct impact on the performance and areas of application. The Hybrid Power System (HPS) has a prominent role in overcoming these challenges with a view to expanding the application fields of UAVs to include further areas such as air taxis and air ambulance services. This work first presents a systematic review of the scientific contributions in the past two decades with the aim of exploring the existing design approaches for HPSs in multi-rotor UAVs. To do this, a Systematic Literature Review (SLR) has been done. The selected articles have been reviewed, analyzed, evaluated, and then classified according to the scope of the study, research trends, design methodologies, main findings/shortcomings, and future work. Retrieved data shows that the Internal Combustion Engine (ICE) and the Proportional-Integral-Derivative (PID) controller were most commonly used. Fuel Cells (FCs) still need more research and experiments to overcome practical constraints, while solar-powered UAVs require more surface areas to absorb large amounts of solar radiation. To keep up-todate with technological advances in this area, this research also surveys, analyzes, and discusses the available commercial models of HPS that can be used in UAVs along with some examples of hybrid-powered UAVs. The intended goal of this paper is to stimulate and help researchers and those interested in the challenges of electric UAVs and guide them to develop this field more efficiently from an industrial/scientific perspective.INDEX TERMS Hybrid power system, hybrid-powered multi-rotor UAV, systematic literature review.