Bridge health monitoring (BHM) has grown as an essential component of the maintenance paradigm in any transportation network around the world. The mostly used visual inspection method has limitations such as inspector bias, inaccessibility in remote areas, need for human physical presence at the bridge location, etc. On the other hand, vibration-based BHM methods require artificial excitation to the bridge. This motivates researchers to explore potential alternatives for BHM. The bridge weigh-in-motion (B-WIM) system has emerged as a promising alternative with the potential to augment traditional BHM techniques. The advantages of B-WIM systems are durability, portability, easy installation, etc. In addition to weight estimation of passing vehicles, it provides other structural informations that are helpful for bridge assessment. It also overcomes the limitations of pavement-based WIM systems. Most importantly, a B-WIM system uses the same components as a standard BHM system, making BHM a by-product and economical compared to a standalone BHM system. With the development of B-WIM theory, recent researches have revealed the feasibility of B-WIM system for BHM. However, the applicability of the B-WIM system for BHM in any type of bridge and condition is limited. Through the fundamentals of B-WIM theory, this paper reviews the existing bridge response-based BHM methods that involved B-WIM algorithm. The findings are discussed in order to identify the remaining challenges and provide insight to the future aspects.