The decentralised, cooperative and self-organising nature of Peer-to-Peer (P2P) systems help to mitigate and even overcome many challenges which overwhelm the traditional client-server approaches. On the other hand, these very characteristics also introduce some novel issues in P2P environments. One of the critical issues is how to build the trust relationship within P2P systems. In this paper, we first discuss the desired properties that need to be considered while building trust in P2P

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... . Then, we analyse two types of attacks-both the ones mitigated by as well as the ones aimed at trust systems. After this, we divide the previous research work on building trust in P2P systems into two broad categories, that is, reputation-based and trade-based. We then review and discuss the advances in this area based on this classification. Finally, we point out some potential research directions in building trust securely in P2P systems.