This review describes the use of Unmanned Aircraft Systems (UAS) for bridge inspection, with an emphasis on Multi-rotor UAS. It depicts the different levels of automation and autonomy during UAS operation and what levels are achieved during inspections. A description of the payload of UAS consisting of the equipment required to acquire data and images is included. It also contains a compendium of the techniques used to create models from images in order to detect failures and perform Structural Health Monitoring (SHM) through techniques, such as: 3D reconstruction, infrared thermography, Structure From Motion (SFM), Convolutional Neural Network (CNN) and others. The software required to apply the mentioned techniques is also mentioned. It subsequently explains the generation of mathematical models to characterize the multirotor and generate efficient trajectories. Finally, the review concludes by describing the operational limitations of UAS and future challenges.