The recent evolution of wireless technology makes wireless devices ever more powerful and intelligent. One trend is that wireless devices are becoming more inexpensive and more diverse. As a result, new technologies make it possible to equip wireless nodes with several radio transmitters/receivers. Each radio may support multiple channels which enable nodes to perform many concurrent communications. Therefore, a new model is needed to capture the new scenario. To foster deploying multiple radio interfaces in wireless devices, we investigate the potential advantages of multi-radio wireless networks over single radio networks. To this end, we introduce the concept called multigraph advantage, through which we analyze properties of multi-radio wireless networks. We show that the multi-radio network has advantages over the collection of separated single radio networks. The first basic property of wireless networks we focus on is the connectivity of the network topology. We show that there is significant gain in connectivity, due to the multi radio setting. Moreover, this gain does not vanish when the size of the network grows. Our experiments show that this gain exists in many different random graph models that capture the wireless network topologies. We then investigate other performance parameters of multi-radio networks, including network latency, packet collision and energy consumption. In this trend, both theoretical results and practical achievements show the advantages of deploying wireless devices with multiple radios. The other trend we deal with is that new wireless technologies enable users and small operators to deploy their own networks and to compete with the large network operators that run traditional wireless networks. Because participants have increased control over their devices, they are free to act on their own interests. Thus, recent trends in the analysis and design of computer network protocols take into account rationally selfish behavior by the different participants of the network. In general, the result of local optimization with conflicting interests does not lead to any type of global optimality or may even paralyze the system completely. In this context we consider two major problems in wireless networks, routing and bandwidth sharing, using the methods of game theory. Both problems are considered in non-cooperative scenarios, where participants are rationally selfish. On the passive side, we study the existence of Nash equilibria, and the system efficiency in the non-cooperative case, in comparison with the cooperative one. On the active side, we propose new algorithms which drive the system into equilibrium points. At these points, no participant has incentive to deviate from the algorithms. Moreover, the algorithms result in globally optimal system performance and a fair sharing of resources among the participants. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]