Centralized file-sharing networks have low reliability, scalability issues, and possess a single point of failure, thus making peer-to-peer (P2P) networks an attractive alternative since they are mostly anonymous, autonomous, cooperative, and decentralized. Although, there are review articles on P2P overlay networks and technologies, however, other aspects such as hybrid P2P networks, modelling of P2P, trust and reputation management issues, coexistence with other existing networks, and so on have not been comprehensively reviewed. In addition, existing reviews were limited to articles published in or before 2012. This paper performs a state-of-the-art literature survey on the emerging research areas of P2P networks, applications and ensuing challenges along with proposed solutions by scholars. The literature search for this survey was limited to the top-rated publisher of scholarly articles. This research shows that issues with security, privacy, the confidentiality of information and trust management will need greater attention, especially in sensitive applications like health services and vehicle to vehicle communication ad hoc networks. In addition, more work is needed in developing solutions to effectively investigate and curb deviant behaviours among some P2P networks.