Recently, there has been a lot of innovative work on cloud-based mobile networks. While distributed computing gives immense chances, it likewise forces a few difficulties. One of the difficulties that current information system administrators and future Fifth Generation (5G) wireless communication are predicting is a gigantic increment in data traffic. It is anticipated based on the vision of Internet of Things (IoT) that the growing 5G wireless communication will meet an extraordinary increment in congestion of calculating and processing of data as IoT incorporated exaggerated applications. A fundamental innovation in the escalating age of 5G is Mobile Edge Computing (MEC). Before sending the data to the cloud server, MEC can upgrade mobile devices by facilitating inventory intensified applications, process huge information and give the distributed computing platform within the radio access network (RAN). Hence, MEC empowers a wide range of utilizations. Without a doubt, the worldview is moving to the future generation network which could turn into a reality with the coming of new mechanical ideas. The actual response of MEC is still in its early stages and requests for steady endeavors from both scholarly and industry networks. With the ever-developing energy utilization for data and wireless communication innovation, the communication nodes and infrastructure undertake a significant job in worldwide greenhouse substance releases. Thus, the improvement of green 5G has become a significant task for the structure and execution of future remote communication. As MEC is a key segment of 5G, the energy efficiency has become a standard worry for the construction of the MEC component. In this chapter, we initially give an all-encompassing outline of MEC, its energy efficient innovation, potentials, needs, and applications. We further sum up exercises gained from energy efficient resource allocation and task offloading. We also talk about difficulties and expected future headings for MEC research.