Mixture of Experts (MoE) has emerged as a promising paradigm for scaling model capacity while preserving computational efficiency, particularly in large-scale machine learning architectures such as large language models (LLMs). Recent advances in MoE have facilitated its adoption in wireless networks to address the increasing complexity and heterogeneity of modern communication systems. This paper presents a comprehensive survey of the MoE framework in wireless networks, highlighting its potential in optimizing resource efficiency, improving scalability, and enhancing adaptability across diverse network tasks. We first introduce the fundamental concepts of MoE, including various gating mechanisms and the integration with generative AI (GenAI) and reinforcement learning (RL). Subsequently, we discuss the extensive applications of MoE across critical wireless communication scenarios, such as vehicular networks, unmanned aerial vehicles (UAVs), satellite communications, heterogeneous networks, integrated sensing and communication (ISAC), and mobile edge networks. Furthermore, key applications in channel prediction, physical layer signal processing, radio resource management, network optimization, and security are thoroughly examined. Additionally, we present a detailed overview of open-source datasets that are widely used in MoE-based models to support diverse machine learning tasks. Finally, this survey identifies crucial future research directions for MoE, emphasizing the importance of advanced training techniques, resource-aware gating strategies, and deeper integration with emerging 6G technologies.