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With the rapid development of electronics, communication networks and information technologies, there are emerging more and more open Internet-based web services and versatile applications. Users or agent entities accomplish their effective interactions and transactions based on the essential trust relations, and the trust assessment would provide secure services, privacy protection and trustworthy decision and for large-scale complicated networks. the basic attributes and represents of trust are firstly presented, and then the trust assessment theories and algorithms are classified and analyzed. the state-of-the-art of trust management, including the trust model, transmission and measure, are detailed discussed in the emerging social networks with small-world feature. Finally, some open issues and challenges of trust assessment are highlighted, in combination with a novel research direction of trust modeling on digital contents share and distribution in multimedia social network.