Wireless data communications, especially to and from portable mobile devices, is one of the fastest growing paradigms in the field of computer communications. This fast paced growth of wireless communication devices is making some communication frequency bands overcrowded. There exists legacy frequency spectrum that remains under utilized. As a result, there are great inefficiencies in how the overall available frequency spectrum is utilized, motivating the need for new technologies to solve this issue. Cognitive Radio (CR) is an emerging technology proposed over the past decade in order to deal with spectrum inefficiency and to help improving wireless communication performance. A CR has the capability to scan across the spectrum to find under utilized channels and use them for communications under some stipulated conditions. A key aspect of CRs is the "cognition" gained through a spectrum scanning process. The benefit of this cognition is apparent and well studied in terms of achieving better communication performance on selected spectrum and detecting the presence of primary users of licensed spectrum. The benefits in terms of reduced energy consumption in secondary users, however, due to easier channel access and less contention have not been quantified in prior work. Spectrum scanning to gain cognition is a power intensive process and the costs incurred in terms of energy lost need to be accounted for. Thus, it is not clear whether a cognitive radio based node would be more energy efficient than any conventional radio node, and if so, under what circumstances. As a result, the focus of this work is on the ad hoc Wireless LAN scenario that works in the highly congested ISM bands. In this dissertation three important contributions to research on ad-hoc WLAN cognitive radios are presented. First, a comprehensive survey on prior research in cognitive radio networks with a focus on the implications for energy consumption is presented. Second, the energy consumption of a radio that uses the CR technique is modeled and analyzed for a static scenario with fixed channel conditions and node populations. As part of this work four novel spectrum scanning algorithms are proposed and analytically evaluated for their energy consumption. Finally, the energy consumption of a radio that employs the CR technique through one of our four spectrum scanning schemes is studied through simulations for dynamic scenarios that include diverse channel conditions and varying node populations.