This paper presents a detailed review of the existing literature on peer-to-peer (P2P) energy trading considering market architectures, trading strategies, and enabling technologies. P2P energy trading enables individual users in the electricity network to act as sellers or buyers and trade energy among each other. To facilitate the discussion on different aspects of P2P energy trading, this paper focuses on P2P market mechanisms, relevant bidding strategies, and auction models. In addition, to solve the energy management problems associated with P2P energy trading, this paper investigates widely used solution methods such as game-theoretic models, mathematical optimisation, as well as more recent machine learning techniques and evaluates them in a critical manner. The outcomes of this investigation along with the identification of the challenges and limitations will allow researchers to find suitable P2P energy trading mechanisms based on different market contexts. Moreover, the discussions on potential future research directions are expected to improve the effectiveness of P2P energy trading technologies.