The rise of Generative AI (GenAI) in recent years has catalyzed transformative advances in wireless communications and networks. Among the members of the GenAI family, Diffusion Models (DMs) have risen to prominence as a powerful option, capable of handling complex, high-dimensional data distribution, as well as consistent, noise-robust performance. In this survey, we aim to provide a comprehensive overview of the theoretical foundations and practical applications of DMs across future communication systems. We first provide an extensive tutorial of DMs and demonstrate how they can be applied to enhance optimizers, reinforcement learning and incentive mechanisms, which are popular approaches for problems in wireless networks. Then, we review and discuss the DM-based methods proposed for emerging issues in future networks and communications, including channel modeling and estimation, signal detection and data reconstruction, integrated sensing and communication, resource management in edge computing networks, semantic communications and other notable issues. We conclude the survey with highlighting technical limitations of DMs and their applications, as well as discussing future research directions.