The Peer-to-Peer (P2P) paradigm of computing has been growing dramatically in popularity over the last decade. Consequently, large amounts of data are being shared among P2P users on a global-scale. Given the inherently untrustworthy nature of P2P networks, this paper provides a perspective concerning trust, privacy and security issues in P2P networks. Additionally, we discuss the applicability of the P2P paradigm to new application domains, the aim being to ensure that the power of the P2P paradigm goes well beyond P2P file-sharing interactions.