Abstract: Fifth generation (5G) cellular networks are expected to achieve high data rates, reduced latency, increased spectrum efficiency, and energy efficiency. Ultra-dense networks (UDNs), a key enabling technology in 5G cellular networks, are envisioned to support the deluge of data traffic located in hotspots and at cell edges, and to enhance quality of experience of mobile users. UDNs can significantly improve the spectrum efficiency and energy efficiency to achieve sustainability of 5G. However, the deployment of a large number of small cells poses new challenges for energy efficiency. Recently, the energy efficiency of UDNs has become a prime concern in the operation and architecture design owing to environmental and economic effects. Therefore, it is significant to study the energy efficiency of UDNs. This survey provided an overview of energy-efficient wireless communications, and reviewed seminal and recent contribution to the state-of-the-art. Therefore, the definitions of energy efficiency, a key performance indicator of the UDNs, are analyzed, which is a foundation for modeling. Four theoretical models, which were often used in the modeling and optimization of energy efficiency, were discussed. These models include stochastic geometry, game theory, optimization theory, and fractional programming theory. Energy-efficient techniques of UDNs were also reviewed. These technologies include energy-efficient deployment and planning, a base station sleeping mode, user association, radio resource management, and transmission. Finally, the most relevant research challenges were addressed, including the theory of energy efficiency of UDNs, architecture of UDNs, the high energy efficiency coverage mechanism of ultra-dense small base stations, the flexible radio resource matching mechanism of UDNs, group behavior modeling of mobile users, and high energy efficiency service methods. This review of the energy-efficient coverage mechanism and flexible radio resource matching mechanism in UDNs provides design guidelines and potential solutions for analytical modeling of future wireless networks.