During the last decade, the efforts in space exploration have increased massively and led to a need for new ways to examine planets and other celestial bodies. The modern tendency is to create spacecraft able to scout the surface from a higher point of view, where drones have shown to be most helpful. Even if the benefits brought by this type of technology are considerable, the challenges are still difficult to overcome. This article presents a comprehensive literature review on drone technologies for planetary exploration, focusing mainly on the difficulties encountered. Considerable complications derive from the unknown environment, affecting most of the design, the mathematical model of the body, its controllability, and overall levels of autonomy. Various solutions to these challenges are proposed based on past and future missions. Furthermore, a look into the future gives an idea of possible technological developments and ways to provide the most efficient aerial exploration of other planets.