The concept of energy-aware communications has spurred the interest of the research community in the most recent years due to various environmental and economical reasons. It becomes indispensable for wireless communication systems to shift their resource allocation problems from optimizing traditional metrics, such as throughput and latency, to an environmental-friendly energy metric. Although cognitive radio systems introduce spectrum efficient usage techniques, they employ new complex technologies for spectrum sensing and sharing that consume extra energy to compensate for overhead and feedback costs. Considering an adequate energy efficiency metric—that takes into account the transmit power consumption, circuitry power, and signaling overhead—is of momentous importance such that optimal resource allocations in cognitive radio systems reduce the energy consumption. A literature survey of recent energy-efficient based resource allocations schemes is presented for cognitive radio systems. The energy efficiency performances of these schemes are analyzed and evaluated under power budget, co-channel and adjacent-channel interferences, channel estimation errors, quality-of-service, and/or fairness constraints. Finally, the opportunities and challenges of energy-aware design for cognitive radio systems are discussed.