IoT is expanded by leveraging social networking ideas to build a social network of interlinked smart devices called Social Objects (SO), and the resulting network is called the Social Internet of Things (SIoT). These SOs have social features that allow them to find other SOs in their environment and establish social interactions with them. Trust Management Systems (TMS) comprehends how the data supplied by the communicating parties must be processed based on the object’s behavior in order to establish reliable autonomous communications. The literature on TMS in SIoT is limited, and the existing paper’s review of issues, challenges, and future directions is not complete. This paper first presents the trust management concepts in SIoT. Second, the existing TMS for SIoT proposed in papers throughout the previous seven years (2017–2023) are categorized as process-based TMS, context-based TMS, blockchain-based TMS, and edge-based TMS. These models are analyzed in terms of trust features, aggregation techniques, trust update mechanisms, trust propagation strategies, evaluation tools, and performance metrics. The percentage of effort exhibited by various TMS in solving issues in SIoT are: residual energy of a node (14%) and scalability (19%) are given less emphasis, while most of the TMS have focused on resiliency against BMA (81%) and BSA (71%). Third, the paper discusses research challenges and future directions investigated by the survey that help the researchers develop a robust, adaptable and resilient TMS.