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Due to the expansion of distributed renewable energy resources, peer to peer energy trading (P2P DET) is expected to be one of the key elements of next generation power systems. P2P DET can provide various benefits such as creating a competitive energy market, reducing power outages, increasing overall efficiency of power systems and supplementing alternative sources of energy according to user preferences. Because of these promising advantages, P2P DET has attracted the attention of several researchers. Current research related to P2P DET include demand response optimization, power routing, network communication, security and privacy. This paper presents a review of the main research topics revolving around P2P DET. Particularly, we present a comprehensive survey of existing demand response optimization models, power routing devices and power routing algorithms. We also identify some key challenges faced in realizing P2P DET. Furthermore, we discuss state of the art enabling technologies such as Energy Internet, Blockchain and Software Defined Networking (SDN) and we provide insights into future research directions.