The stringent requirements of a 1,000 times increase in data traffic and one millisecond round trip latency have made limiting the potentially tremendous ensuing energy consumption one of the most challenging problems for the design of the upcoming fifth-generation (5G) networks. To enable sustainable 5G networks, new technologies have been proposed to improve the system energy efficiency and alternative energy sources are introduced to reduce our dependence on traditional fossil fuels. In particular, various 5G techniques target the reduction of the energy consumption without sacrificing the quality-of-service. Meanwhile, energy harvesting technologies, which enable communication transceivers to harvest energy from various renewable resources and ambient radio frequency signals for communi- cation, have drawn significant interest from both academia and industry. In this article, we provide an overview of the latest research on both green 5G techniques and energy harvesting for communication. In addition, some technical challenges and potential research topics for realizing sustainable green 5G networks are also identified. ; Comment: Submitted for possible publication