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In recent years, there has been a growing interest in green cellular networks for the sake of reducing the energy dissipated by communications and networking devices, including the base stations (BSs) and battery-powered user terminals (UTs). This paper investigates the joint employment of cognition and cooperation techniques invoked for improving the energy efficiency of cellular networks. To be specific, the cellular devices first have to identify the unused spectral bands (known as spectrum holes) using their spectrum sensing functionality. Then, they cooperate for exploiting the detected spectrum holes to support energy-efficient cellular communications. Considering the fact that contemporary terminals (e.g., smart phones) support various wireless access interfaces, we exploit either the Bluetooth or the Wi-Fi network operating within the spectrum holes for supporting cellular communications with the intention of achieving energy savings. This approach is termed cognitive network cooperation, since different wireless access networks cognitively cooperate with cellular networks. In order to illustrate the energy efficiency benefits of using both cognition and cooperation, we study the cooperation between television stations (TVSs) and BSs in transmitting to UTs relying on an opportunistic exploitation of the TV spectrum, where the unused TV spectral band is utilized in an opportunistic way, depending on whether it is detected to be idle (or not). It is shown that for a given number of information bits to be transmitted, the total energy consumed is significantly reduced, when both cognition and cooperation are supported in cellular networks, as compared with the conventional direct transmission, pure cognition, and pure cooperation.