Radio resource management is important for wireless communication networks. Game theory has been extensively used to model, analyze, and design interactive behaviors and the strategic decision‐making for radio resource management. It is known that utility function is one of the critical elements in a game, which characterizes the preferred relationship of the rational players and is a function of the action of players and their opponents. We first overview the basics of game theory and utility functions. We then present a taxonomy of utility functions with respect to different types of players, the nature of actions, and preferences in terms of the fairness, quality of service, and quality of experience. We provide some insights based on the taxonomy of utility functions, which provides the readers with a comprehensive view. Following that, we also discuss other types of traffic‐aware utility functions with different fairness and the potential and super modular game‐theoretic utility functions. In addition, we summarize the desired properties and observations for the design of suitable utility functions. Finally, we investigate impacts of the pricing in utility functions. This article ends with the conclusions and a promising view on open problems and challenges with possible future research directions.