Trustworthy and explainable structural health monitoring (SHM) of bridges is crucial for ensuring the safe maintenance and operation of deficient structures. Unfortunately, existing SHM methods pose various challenges that interweave cognitive, technical, and decision-making processes. Recent development of emerging sensing devices and technologies enables intelligent acquisition and processing of massive spatiotemporal data. However, such processes always involve human-in-the-loop (HITL), which introduces redundancies and errors that lead to unreliable SHM and service safety diagnosis of bridges. Comprehending human-cyber (HC) reliability issues during SHM processes is necessary for ensuring the reliable SHM of bridges. This study aims at synthesizing studies related to HC reliability for supporting the trustworthy and explainable SHM of bridges. The authors use a bridge inspection case to lead a synthesis of studies that examined techniques relevant to the identified HC reliability issues. This synthesis revealed challenges that impede the industry from monitoring, predicting, and controlling HC reliability in bridges. In conclusion, a research road map was provided for addressing the identified challenges.