As the era of big data arrives, traditional artificial intelligence algorithms have difficulty processing the demands of massive and diverse data. Mixture of experts (MoE) has shown excellent performance and broad application prospects. This paper provides an in-depth review and analysis of the latest progress in this field from multiple perspectives, including the basic principles, algorithmic models, key technical challenges, and application practices of MoE. First, we introduce the basic concept of MoE and its core idea and elaborate on its advantages over traditional single models. Then, we discuss the basic architecture of MoE and its main components, including the gating network, expert networks, and learning algorithms. Next, we review the applications of MoE in addressing key technical issues in big data. For each challenge, we provide specific MoE solutions and their innovations. Furthermore, we summarize the typical use cases of MoE in various application domains. This fully demonstrates the powerful capability of MoE in big data processing. We also analyze the advantages of MoE in big data environments. Finally, we explore the future development trends of MoE. We believe that MoE will become an important paradigm of artificial intelligence in the era of big data. In summary, this paper systematically elaborates on the principles, techniques, and applications of MoE in big data processing, providing theoretical and practical references to further promote the application of MoE in real scenarios.