Maps are broadly relevant across various fields, serving as valuable tools for presenting spatial phenomena and communicating spatial knowledge. However, map-making is still largely confined to those with expertise in GIS and cartography due to the specialized software and complex workflow involved, from data processing to visualization. While generative AI has recently demonstrated its remarkable capability in creating various types of content and its wide accessibility to the general public, its potential in generating maps is yet to be fully realized. This paper highlights the key applications of generative AI in map-making, summarizes recent advancements in generative AI, identifies the specific technologies required and the challenges of using current methods, and provides a roadmap for developing a generative mapping system (GMS) to make map-making more accessible.