Bridges play a crucial role in modern societies, regardless of their culture, geographical location, or economic development. The safest, economical, and most resilient bridges are those that are well managed and maintained. In the last three decades, structural health monitoring (SHM) has been a promising tool in management activities of bridges as potentially it permits one to perform condition assessment to reduce uncertainty in the planning and designing of maintenance activities as well as to increase the service performance and safety of operation. The general idea has been the transformation of massive data obtained from monitoring systems and numerical models into meaningful information. To deal with large amounts of data and perform the damage identification automatically, SHM has been cast in the context of the statistical pattern recognition (SPR) paradigm, where machine learning plays an important role. Meanwhile, recent technologies have unveiled alternative sensing opportunities and new perspectives to manage and observe the response of bridges, but it is widely recognized that bridge SHM is not yet fully capable of producing reliable global information on the presence of damage. While there have been multiple review studies published on SHM and vibration-based structural damage detection for wider scopes, there have not been so many reviews on SHM of bridges in the context of the SPR paradigm. Besides, some of those reviews become obsolete quite fast, and they are usually biased towards applications falling outside of bridge engineering. Therefore, the main goal of this article is to summarize the concept of SHM and point out key developments in research and applications of the SPR paradigm observed in bridges in the last three decades, including developments in sensing technology and data analysis, and to identify current and future trends to promote more coordinated and interdisciplinary research in the SHM of bridges.