Ensuring security in a distributed environment such as P2P networks is a critical issue nowadays. Nevertheless, it is in those kind of scenarios in which entities can enter or leave the community whenever they want, where traditional mboxsecurity schemes can not always be applied. Specifically, the use of a PKI (Public Key Infrastructure) may be unacceptable within highly distributed systems. Therefore, modeling concepts like trust and reputation may result very helpful and useful when trying to gain a certain level of security and confidence among inter-operating entities. Thus, this chapter presents a review of some of the most representative trust and reputation models for P2P networks, discussing their main characteristics and also their weaknesses and deficiencies. Open issues and challenges associated with them will be also covered.