The utilization of small unmanned aerial vehicles (SUAVs), commonly known as drones, has increased drastically in various industries in the past decade. Commercial drones face challenges in terms of safety, durability, flight performance, and environmental effects such as the risk of collision and damage. Biomimetics, which is inspired by the sophisticated flying mechanisms in aerial animals, characterized by robustness and intelligence in aerodynamic performance, flight stability, and low environmental impact, may provide feasible solutions and innovativeness to drone design. In this paper, we review the recent advances in biomimetic approaches for drone development. The studies were extracted from several databases and we categorized the challenges by their purposes—namely, flight stability, flight efficiency, collision avoidance, damage mitigation, and grasping during flight. Furthermore, for each category, we summarized the achievements of current biomimetic systems and then identified their limitations. We also discuss future tasks on the research and development associated with biomimetic drones in terms of innovative design, flight control technologies, and biodiversity conservation. This paper can be used to explore new possibilities for developing biomimetic drones in industry and as a reference for necessary policy making.