In recent years, deep learning technology has developed rapidly, demonstrating powerful capabilities in data processing, pattern recognition, and information interpretation, which brings revolutionary potential for efficiency improvements in optimization algorithms. The application of deep learning methods to optimize the design of electromagnetic metamaterials has become a hot research topic and has made significant progress. Against this backdrop, we review existing inverse design methods for electromagnetic metamaterials, including a brief overview of the current status and limitations of classical iterative algorithms, as well as various deep learning-based design techniques. We specifically discuss the application scope, advantages, limitations, and latest research advancements of deep learning-based design techniques. We highlight diverse neural network architectures proposed in the research and their application examples in electromagnetic metamaterial optimization. We also delve into the roles, limitations, and potential applications of these optimization methods in practical design. Finally, we look forward to the future development direction of electromagnetic metamaterial design and its deep integration with artificial intelligence technology.