In this article, we investigate self-organizing optimization for cognitive small cells (CSCs), which have the ability to sense the environment, learn from historical information, make intelligent decisions, and adjust their operational parameters. By exploring the inherent features, some fundamental challenges for self-organizing optimization in CSCs are presented and discussed. Specifically, the dense and random deployment of CSCs brings about some new challenges in terms of scalability and adaptation; furthermore, the uncertain, dynamic and incomplete information constraints also impose some new challenges in terms of convergence and robustness. For providing better service to the users and improving the resource utilization, four requirements for self-organizing optimization in CSCs are presented and discussed. Following the attractive fact that the decisions in game-theoretic models are exactly coincident with those in self-organizing optimization, i.e., distributed and autonomous, we establish a framework of game-theoretic solutions for self-organizing optimization in CSCs, and propose some featured game models. Specifically, their basic models are presented, some examples are discussed and future research directions are given.