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With explosive growth of high-data-rate applications, more and more energy is consumed in wireless networks to guarantee quality of service. Therefore, energy-efficient communications have been paid increasing attention under the background of limited energy resource and environmental- friendly transmission behaviors. In this article, basic concepts of energy-efficient communications are first introduced and then existing fundamental works and advanced techniques for energy efficiency are summarized, including information-theoretic analysis, OFDMA networks, MIMO techniques, relay transmission, and resource allocation for signaling. Some valuable topics in energy-efficient design are also identified for future research.