Using aerial platforms for Non-Destructive Inspection (NDI) of large and complex structures is a growing field of interest in various industries. Infrastructures such as: buildings, bridges, oil and gas, etc. refineries require regular and extensive inspections. The inspection reports are used to plan and perform required maintenance, ensuring their structural health and the safety of the workers. However, performing these inspections can be challenging due to the size of the facility, the lack of easy access, the health risks for the inspectors, or several other reasons, which has convinced companies to invest more in drones as an alternative solution to overcome these challenges. The autonomous nature of drones can assist companies in reducing inspection time and cost. Moreover, the employment of drones can lower the number of required personnel for inspection and can increase personnel safety. Finally, drones can provide a safe and reliable solution for inspecting hard-to-reach or hazardous areas. Despite the recent developments in drone-based NDI to reliably detect defects, several limitations and challenges still need to be addressed. In this paper, a brief review of the history of unmanned aerial vehicles, along with a comprehensive review of studies focused on UAV-based NDI of industrial and commercial facilities, are provided. Moreover, the benefits of using drones in inspections as an alternative to conventional methods are discussed, along with the challenges and open problems of employing drones in industrial inspections, are explored. Finally, some of our case studies conducted in different industrial fields in the field of Non-Destructive Inspection are presented.