Mixture-of-Experts (MoE) presents a naturally compatible and scalable framework for multimodal learning, demonstrating strong adaptability across diverse modalities and tasks. Despite its growing success, a comprehensive and systematic review on the MoE metho addressing multimodal challenges remains lacking. Existing surveys tend to evaluate either multimodal learning or MoE independently from method taxonomy, overlooking the unique interplay between them. This survey fills that gap by answering a central question: \textit{How does MoE effectively resolve multimodal challenges?} We approach this from three key perspectives: (1) \textbf{MoE as an Efficient Multimodal Engine:} enabling scalable multimodal modeling by decoupling computational cost from parameter growth and mitigating modality redundancy through selective expert activation; (2) \textbf{MoE as a Multimodal Representation Learner:} integrating complementary multi-opinion expert knowledge to enrich alignment and interaction representations; and (3) \textbf{MoE as a Multimodal Adapter:} providing a modular and flexible mechanism to model imperfect data scenarios such as modality imbalance and missing modality. Through our extensive literature review, we identify critical research gaps, including interpretable routing, expert communication, modality integration, and lifelong multimodal learning. We position this survey as a foundation for future research toward interpretable and sustainable multimodal Mixture-of-Experts system.