Edge computing is an emerging paradigm to meet the ever-increasing computation demands from pervasive devices such as sensors, actuators, and smart things. Though the edge devices can execute complex applications, it is necessary for some applications to migrate to centralized servers. By offloading the computation from the edge nodes to the edge servers or cloud servers, the quality of computation experience could be greatly improved. However, it may cause delay and increase network overheads, and energy consumption eventually. Therefore, an optimal offloading strategy should take into account what task should be offloaded, when to offload and where to offload to avoid the overheads. Thus, it is important to tradeoff between energy consumption, computation delay and throughput when the system makes the computation offloading to achieve high energy efficiency. In this paper, we conduct a survey of energy aware edge computing, including the existing work on computation offloading frameworks and strategies in edge computing. Specifically, we describe the strategies from the perspective of energy aware offloading, energy optimization offloading and offloading algorithms.