Reputation systems offer a viable solution to the old problem of encouraging trustworthy behavior in online communities. Their key presumptions are that the participants of an online community engage in repeated interactions and that the information about their past doings is informative of their future performance and as such will influence it. Thus, collecting, processing, and disseminating the feedback about the participants' past behavior is expected to boost their trustworthiness. We investigate and classify the possibilities appeared so far in the literature to do this in the context of P2P networks. We identify three broad classes of approaches: social networks formation, probabilistic estimation techniques and game-theoretic reputation models. They differ greatly in the accompanying trust semantics, mainly reflected in the possibilities offered to the decision makers, and the implementation overhead they incur. The paper bridges the gap between the existing works on trust and reputation management in decentralized networks, driven by the characteristics of the target environment and the formal game-theoretic treatment of reputation, aiming at a clear and analytical decision making. This view leads us to identify the open research issues, oriented towards both efficient and analytical usage of reputation to build trust in P2P networks.