•A review on motion magnification-based vibration measurement of structures is presented.•Basic principles of the motion magnification methods commonly used are reviewed.•Major challenges and the research works to address these challenges are summarized.•Representative applications of motion magnification techniques are reviewed.•Research prospects for motion magnification-based vibration measurement are introduced. Vibration measurement plays an important role in the inspection and monitoring of civil structures. In recent years, the computer vision (CV)-based method has gained significant popularity in the field of vibration measurement for civil structures due to its inherent advantages, such as non-contact, low cost, long-distance measurement, and ease of implementation. However, those traditional CV-based methods are only suitable for situations with large vibration amplitude. The vibration of some civil structures is usually small especially under environmental excitation, which poses challenges for the traditional CV-based methods. The motion magnification (MM) technique has emerged as an effective solution for small-amplitude vibration measurement. Therefore, this study comprehensively reviews the MM technique for video-based vibration measurement of civil structures. First, the principles and characteristics of some representative MM techniques are introduced. Then, three major challenges encountered in vibration measurement of civil structures using MM techniques are summarized, and the research work to address these challenges is reviewed. Finally, the applications of MM techniques on various civil structures including bridges, cables, buildings, wind turbines and dams are summarized. This review can provide guidance to researchers and engineers in selecting suitable MM methods for vibration measurement of civil structures.