The work aims to review and summarize the current state of research on generative artificial intelligence-assisted cultural and creative design methods and discuss the trends in future generative AI-assisted design methods. Literature analysis, comparative research, and case study analysis were adopted as the main research methods. Through the analysis on the functional differences and technological integration between cultural and creative design methods and concepts related to generative AI, the applications and limitations of the integration were summarized. Relevant literature from the CNKI database in China was selected for analysis, covering the early stages of generative AI involvement in cultural and creative design, the processing stage and the entire workflow. Based on clarifying the current state of research on generative AI in cultural and creative design, the trends in three aspects of design methods under generative AI were summarized, namely digitalization, personalization, and integration of cultural and creative design methods. Generative artificial intelligence can enhance the quality and efficiency of cultural and creative design methods in terms of specific methods, processes and content. With the continuous development of generative AI technologies, the design industry serving culture is expected to enter an era of explosive creativity, providing more innovative and futuristic ideas for culture.