With the popularization of wireless multimedia communications, the wireless traffic is predicated to be increased more than 1000 time in the next decade. Some new technologies, e.g., massive multi-input multi-output antennas, millimeter wave and small cell networks are developed to support high speed wireless transmission in future fifth generation (5G) mobile communication systems. On the other hand, it is a great challenge how to face the quick growth of energy consumption in 5G mobile communication networks due to the massive wireless traffic. However, detailed investigation of the energy efficiency of 5G mobile communication networks from three aspects of theory models, technology developments and applications is surprisingly rare in the open literature. Fortunately, the scholarly writing, 5G Green mobile communication networks, published by Publishing House of Electronics Industry in November 2016, points out the directions and research advance of 5G green mobile communication networks.