The detection of damage in bridges subjected to moving loads has attracted increasing attention in the field of structural health monitoring. Processing the dynamic responses induced by moving loads to characterize damage is the key to identifying damage in bridges. On this topic, various methods of processing dynamic responses to moving loads have been developed in recent decades, with respective strengths and weaknesses. These methods appear in different applications and literatures and their features have not been comprehensively surveyed to form a profile of this special area. To address this issue, this study presents a comprehensive survey of methods for identifying damage by processing dynamic responses of cracked bridges subjected to moving loads. First, methods utilizing the Fourier transform to process dynamic responses to moving loads for damage detection in bridges are examined. Second, methods using wavelet transform to process the dynamic responses to moving loads for damage characterization are examined. Third, methods of employing the Hilbert-Huang transform to process the dynamic responses to moving loads for damage identification are examined. Fourth, methods of dynamic response-driven heuristic interrogation of damage in bridges subjected to moving loads are examined. Finally, we recommend future research directions for advancing the development of damage identification relying on processing dynamic responses to moving loads. This study provides a profile of the state-of-the-art and state-of-the-use of damage identification in bridges based on dynamic responses to moving loads, with the primary aim of helping researchers find crucial points for further exploration of theories, methods, and technologies for damage detection in bridges subjected to moving loads.