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The success of Artificial Intelligence (AI) in multiple disciplines and vertical domains in recent years has promoted the evolution of mobile networking and the future Internet toward an AI-integrated Internet-of-Things (IoT) era. Nevertheless, most AI techniques rely on data generated by physical devices (e.g., mobile devices and network nodes) or specific applications (e.g., fitness trackers and mobile gaming). To bypass this circumvent, Generative AI (GAI), a.k.a. AI-generated content (AIGC), has emerged as a powerful AI paradigm; thanks to its ability to efficiently learn complex data distributions and generate synthetic data to represent the original data in various forms. This impressive feature is projected to transform the management of mobile networking and diversify the current services and applications provided. On this basis, this work presents a concise tutorial on the role of GAIs in mobile and wireless networking. In particular, this survey first provides the fundamentals of GAI and representative GAI models, serving as an essential preliminary to the understanding of the applications of GAI in mobile and wireless networking. Then, this work provides a comprehensive review of state-of-the-art studies and GAI applications in network management, wireless security, semantic communication, and lessons learned from the open literature. Finally, this work summarizes the current research on GAI for mobile and wireless networking by outlining important challenges that need to be resolved to facilitate the development and applicability of GAI in this edge-cutting area.