In this paper, we review radio resource optimization methods for energy-efficient wireless communication in links and networks using the Orthogonal Frequency Division Multiplexing (OFDM) and Orthogonal Frequency Division Multiple Access (OFDMA) techniques. We first consider the energyefficiency metrics and optimization goals. We discuss the increasingly complex systems, starting from (i) a single OFDM link, (ii) an OFDMA single-hop network to (iii) multi-hop relay OFDMA interference networks.In each case, we elaborate on the transmission rate estimation, power consumption modelling, existing optimization constraints and the optimization solutions. Specifically, in the power-consumption modelling, we include the signal-processing (and related computing) power. We discuss the practicality of the considered solutions. We also touch upon the problem of nonlinear power amplifier characteristics (causing distortions typical for OFDM signals) to be taken into account for energy-efficient resource allocation. We discuss trade-offs and provide recommendations for future energy-efficient OFDM networks design. We also discuss the future works and challenges in the context of energy efficiency resource allocation for OFDM/OFDMA and their derivative techniques. We conclude that the presented design practices should include computational awareness in the networks to trade-off between information communication, information processing and the required network management energy-efficiency.