Bridges are often located in harsh environments and are thus extremely susceptible to damage. If the initial damage is not detected in time, it can develop further causing safety hazards. Therefore, accurate detection of bridge damage is an important topic. In recent years, artificial intelligence technology has been developed rapidly, especially machine learning algorithms, which have shown amazing results in various fields while it also received attention in bridge inspection. This paper summarizes the progress of bridge damage detection research related to artificial intelligence techniques between 2015 and 2021. For structural health monitoring, sensing data is the basis for various data processing methods. The strength and weakness of the sensing data itself directly affect the effectiveness of subsequent processing methods. As a result, this paper classifies bridge damage detection studies into six categories from the types of sensing data: visual image, point cloud, infrared thermal imaging, ground-penetrating radar, vibration response, and other types of data. These six types of damage detection methods were reviewed and summarized respectively. Finally, challenges and future trends were discussed.