This thesis studies fairness in wireless networks. Unlike wired networks, the wireless medium presents many unique challenges. Foremost is the uncertainty associated with a time-varying physical channel. Consequently, we utilize a model that incorporates such variations and uncertainty. The main claim of this work is for a wireless network, fairness can only be achieved in the time-asymptotic sense, due to an inability to accurately measure the medium. As an example, we first present protocols that exhibit asymptotic convergence for distributed multiband networks. We then show that even for the straightforward task of centralized scheduling, if short-term fairness is desired, a guarantee of fairness results in zero throughput. Therefore, we present a concept of ϵ-fairness, where limited tolerance for unfairness permits increased spectral efficiency. We apply this concept to the scheduling problem, and show how it stimulates new design philosophies for realistic fair wireless networks.