Structural health monitoring systems have been employed throughout history to assess the structural responses of bridges to both natural and man-made hazards. Continuous monitoring of the integrity and analysis of the dynamic characteristics of bridges offers a solution to the limitations of visual inspection approaches and is of paramount importance for ensuring long-term safety. This review article provides a thorough, straightforward examination of the complete process for performing operational modal analysis on bridges, covering everything from data collection and preprocessing to the application of numerous modal identification techniques in both the time and frequency domains. It also incorporates advanced methods to address and overcome challenges encountered in previous approaches. The paper is distinguished by its thorough examination of various methodologies, highlighting their specific advantages and disadvantages, and providing concrete illustrations of their implementation in practical settings.