The emergence of novel wireless networking paradigms such as small cell and cognitive radio networks has forever transformed the way in which wireless systems are operated. In particu- lar, the need for self-organizing solutions to manage the scarce spectral resources has become a prevalent theme in many emerging wireless systems. In this article, the first comprehensive tutorial on the use of matching theory, a Nobel Prize winning framework, for resource manage- ment in wireless networks is developed. To cater for the unique features of emerging wireless net- works, a novel, wireless-oriented classification of matching theory is proposed. Then the key solu- tion concepts and algorithmic implementations of this framework are exposed. The developed concepts are applied in three important wireless networking areas in order to demonstrate the usefulness of this analytical tool. Results show how matching theory can effectively improve the performance of resource allocation in all three applications discussed.