With years of tremendous traffic and energy consumption growth, green radio has been valued not only for theoretical research interests but also for the operational expenditure reduction and the sustainable development of wireless communications. Fundamental green tradeoffs, served as an important framework for analysis, include four basic relationships: spectrum efficiency (SE) versus energy efficiency (EE), deployment efficiency (DE) versus energy efficiency (EE), delay (DL) versus power (PW), and bandwidth (BW) versus power (PW). In this paper, we first provide a comprehensive overview on the extensive on-going research efforts and categorize them based on the fundamental green tradeoffs. We will then focus on research progresses of 4G and 5G communications, such as orthogonal frequency division multiplexing (OFDM) and non-orthogonal aggregation (NOA), multiple input multiple output (MIMO), and heterogeneous networks (HetNets).We will also discuss potential challenges and impacts of fundamental green tradeoffs, to shed some light on the energy efficient research and design for future wireless networks.Along with the dramatic traffic explosion, it is also promising to see that the next generation (5G) wireless communications shall include people-to-machine and machine-to-machine communications [23] in order to facilitate more flexible networked social information sharing. As a result, numerous sensors, accessories, or even tools may become the communication entities and the associated running applications over wireless networks will diverge. As reported in [24], wireless communications shall support up to millions of applications and billions of subscribers by year 2020, which is nearly 100 times of today's network. Consequently, with the surprisingly expanding demands for wireless transmission and supporting equipment, the network power consumption is no longer sustainable and the green radio technology becomes essential [25]. A flagship 5G research project from European Union, named Mobile April 28, 2016 DRAFT denote SE, EE and DE, respectively 2 .1 Since we mainly focus on the physical layer transmission, we only adopt the transmission delay here to characterize the delay-power tradeoff which can be regarded as a theoretical limit. 2 We note that area energy efficiency is also another important performance metric for cellular networks. Since it is more related with the cell size, we will emphasize it in heterogeneous networks in Section V. April 28, 2016 DRAFT In the practical systems, however, the tradeoff curves may behave differently. For example, if the circuit power consumption, P c , is considered in the EE evaluation, then η EE = W P +Pc log 2 1 + P W N 0 and the corresponding SE-EE/DE-EE tradeoff curves will be with a bell shape [16] as shown in Fig. 1. BW-PW/DL-PW tradeoffs under the circuit power assumptions have been also discussed in [16]. In particular, several open issues have been raised in [16], including tradeoff analysis for multi-cell systems and HetNet architectures.Four fundamental gr...