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Cognitive functions in wireless network nodes are beneficial for leveraging intricate trade-offs among energy efficiency, performance and practicality. There are two fundamental but entangled aspects of cognitive radios in the green communications context: leveraging CRs for energy efficiency and operation of CRs with energy efficiency. In practice, these two objectives overlap since the improvement of energy efficiency with CRs require efficient CRs, whereas efficient wireless communications require cognitive abilities at different network components and protocols. However, there are intrinsic challenges such as hardware complexity, algorithmic problems, and design trade-offs. In this article we present and discuss these issues to highlight the case of CRs for green wireless communication systems. Additionally, some fundamental trade-offs that emerge from these challenges and their impact on greening communications via cognitive functions are outlined.