With the development of Information and Communication Technologies, trust has been applied more and more in various scenarios. At the same time, different organizations have published a series of trust frameworks to support the implementation of trust. There are also academic paper discussing about these trust standards, however, most of them only focus on a specific application. Unlike existing works, this paper provides an overview of all current available trust standards related to communication networks and future digital world from several main organizations. To be specific, this paper summarizes and organizes all these trust standards into three layers: trust foundation, trust elements, and trust applications. We then analysis these trust standards and discuss their contribution in a systematic way. We discuss the motivations behind each current in forced standards, analyzes their frameworks and solutions, and presents their role and impact on communication works and future digital world. Finally, we give our suggestions on the trust work that needs to be standardized in future.