Flying robots popularly known as drones or UAVs are emerging technologies of the current era. A significant amount of research work has been undertaken in this area in the last few years. Considering the current scenario where aerial vehicles are taking a major part of the market it is important to have an effective and robust design of flying robots. This paper aims to examine the categories of flying robots based on the features that include a range from petite to large and its body structure, wing designs, tail design, propulsion system, and gripper mechanisms along with the associated materials and manufacturing techniques. Again the work is intended to review the respective challenges faced by each category. Mostly the challenges faced by flying robots are design challenges, material selection, and fabrication challenges which are discussed in the paper. In this paper, we have summarized various designs of flying robots developed to date as well as we have focused on major features to be taken care of while designing flying robots. This paper has tried to focus on different design aspects and challenges faced by flying robots so that further research can be carried out to develop effective flying robots in the future.