The rapidly increasing interest from various verticals for the upcoming 5th generation (5G) networks expect the network to support higher data rates and have an improved quality of service. This demand has been met so far by employing sophisticated transmission techniques including massive Multiple Input Multiple Output (MIMO), millimeter wave (mmWave) bands as well as bringing the computational power closer to the users via advanced baseband processing units at the base stations. Future evolution of the networks has also been assumed to open many new business horizons for the operators and the need of not only a resource efficient but also an energy efficient ecosystem has greatly been felt. The deployment of small cells has been envisioned as a promising answer for handling the massive heterogeneous traffic, but the adverse economic and environmental impacts cannot be neglected. Given that 10% of the world’s energy consumption is due to the Information and Communications Technology (ICT) industry, energy-efficiency has thus become one of the key performance indicators (KPI). Various avenues of optimization, game theory and machine learning have been investigated for enhancing power allocation for downlink and uplink channels, as well as other energy consumption/saving approaches. This paper surveys the recent works that address energy efficiency of the radio access as well as the core of wireless networks, and outlines related challenges and open issues.