• A comprehensive review of existing research and pilot projects on P2P energy trading. • Detailed analysis of the implementation methodologies with mathematical formulations. • Discussion on the developed P2P testbed and live demonstration projects. • Directions for future research work in developing P2P energy trading frameworks. Energy sector is undergoing a massive transformation that includes key aspects such as integrating renewables, improving operational efficiency, leveraging smart grid infrastructure, and handling the dynamics of transactive energy; all of which necessitates ecosystem players to refine their role, devise efficient regulatory/policy frameworks, and experiment with new business models. Given these circumstances, Peer-to-Peer (P2P) energy trading appears to be one of the viable solutions in which an end-user can sell/buy power to/from other users instead of fully relying on the utility for the same. However, the implementation of P2P energy trading in the distribution networks introduce new challenges, such as network constraint violations, increased communication requirements, compromised end-user privacy, the threat to the financial viability of the utility companies, etc. Various pilot projects and research are being carried out at different levels worldwide in this regard. This paper provides a detailed analysis of the existing research and implementation activities on P2P energy trading, and suggests potential future research avenues. Readers gain an understanding of P2P energy trading frameworks, implementation methodologies, and demonstration projects through this article.