Recently, reconfigurable drones have gained particular attention in the field of automation and flying robots. Unlike the conventional drones, they are characterized by a variable mechanical structure in flight, geometric adaptability, aerial reconfiguration, high number of actuators and control inputs, and variable mathematical model. In addition, they are exploited to flight in more cluttered environments, avoid collisions with obstacles, transport and grab objects, cross narrow and small spaces, decrease different aerial damages, optimize the consumed energy, and improve agility and maneuverability in flight. Moreover, these new drones are considered as a viable solution to provide them with specific and additional functionalities. They are a promising solution in the near future, since they allow increasing considerably the capabilities and performance of classical drones in terms of multi-functionalities, geometric adaptation, design characteristics, consumed energy, control, maneuverability, agility, efficiency, obstacles avoidance, and fault tolerant control. This paper explores very interesting and recent research works, which include the classification, the main characteristics, the various applications, and the existing designs of this particular class of drones. Besides, an in-depth review of the applied control strategies will be presented. The links of the videos displaying the results of these researches will be also shown. A comparative study between the different types of flying vehicles will be established. Finally, several new challenges and future directions for reconfigurable drones will be discussed.