Edge computing is expected to enable the cloud computing services in proximity and leverage the computational capacities at the edge of a network. Driven by massive data-hungry and energy-hungry applications, future wireless networks will need to provide various cloud-based multimedia services in a »greener» manner. However, limited computing capacity, wireless resources, and power supply prevent edge computing from evolving and maturing in terms of high sustainability and energy efficiency. In this article, we attempt to further improve the energy-efficient communication in mobile edge computing by proposing a device-to-device (D2D) offloading architecture. The D2D technique, in line with mobile edge computing, is responsible for offloading wireless traffic as well as computational tasks. Cooperative relay-aided transmission is also used in this architecture to pursue further improvements in a multi-cell scenario. Finally, offloading and balancing technologies are introduced to increase the total energy efficiency, decrease the inter/ intra-cell interference, deal with traffic/computational congestion, and provide better services to end users. © 1979-2012 IEEE.