The rapid growth of Internet of Things (IoT) devices and edge computing (EC) has improved efficiency, productivity, and quality of life across various sectors. However, these developments also pose significant challenges, particularly in trust and resource management. This paper conducts a comprehensive literature review by examining existing relevant studies to identify recent developments and insights as well as challenges and potential research directions to guide future research. The findings revealed the importance of dynamic trust management models, real-time assessments, and the integration of machine learning and blockchain technologies in increasing network security and reliability. In addition, it highlights innovative resource management strategies using EC and fog computing to optimize resource allocation and system scalability. While advancements have been made in trust and resource management, challenges like scalability, high task volumes, and security remain. The study emphasizes the need for continuous efforts to develop secure, efficient, and reliable IoT and EC systems.