Structural monitoring of bridges is commonly carried out using conventional methods. However, with the advancements in the internet of things (IoT) and digital twin (DT) technologies, this process has been revolutionized. The implementation of IoT enables enhanced sustainability by monitoring various parameters through interconnected devices and sensors. Simultaneously, DT technology creates a synchronized virtual representation of the physical bridges, improving safety, maintenance, and decision-making. This review paper explores foundational concepts of IoT and DT in bridge monitoring, discussing the synergy between DT and IoT for heightened precision in damage detection. It also covers innovative methodologies such as photogrammetry, terrestrial laser scanning, ground penetrating radar, building information modeling, and unmanned aerial vehicles/drones. These methodologies produce detailed 3D models, improving precision, practicality, and efficacy in the monitoring process. The paper serves as a guide for researchers and practitioners, illustrating a progression from foundational concepts to the state-of-the-art technologies. This envisions a future where bridges are monitored with unprecedented accuracy to ensure safer and more resilient infrastructure on a global scale.