Scarcity of the frequency spectrum is a major problem in wireless networks, but it is often due to the static allocation rules currently implemented by regulators. There is a major research effort underway in computer science and engineering to overcome this problem. From an algorithmic perspective, a variety of interesting new variants of independent set and coloring problems arise in this setting. This talk will survey some of our recent work in this area on design and analysis of algorithms with connections to game theory. In particular, a focus are learning algorithms for distributed medium access and more centralized approaches for spectrum auctions. Our goal is to design efficient approximation algorithms and analyze their performance in terms of user incentives and provable bounds for running time and social welfare.