The emergence of novel wireless networkingparadigms such as small cell and cognitive radionetworks has forever transformed the way inwhich wireless systems are operated. In particular,the need for self-organizing solutions tomanage the scarce spectral resources has becomea prevalent theme in many emerging wirelesssystems. In this article, the first comprehensivetutorial on the use of matching theory, a NobelPrize winning framework, for resource managementin wireless networks is developed. To caterfor the unique features of emerging wireless networks,a novel, wireless-oriented classification ofmatching theory is proposed. Then the key solutionconcepts and algorithmic implementationsof this framework are exposed. The developedconcepts are applied in three important wirelessnetworking areas in order to demonstrate theusefulness of this analytical tool. Results showhow matching theory can effectively improve theperformance of resource allocation in all threeapplications discussed