The research illustrates multiple experiences and strategies adopted in museums and in the world of cultural heritage in the field of digital storytelling to guide the future design of narrative digital solutions. Its aim is to provide as complete a picture as possible of the different solutions set in this specific sector of the field of cultural communication, their uses, and the accessibility of culture. It identifies and analyzes 14 types of digital storytelling: oral, written, video, visual, animated, interactive, Immersive, Social Media Storytelling, Participative, Generative, Geo-Storytelling, Multimedia Mobile Storytelling, Crossmedia and Transmedial storytelling. Finally, a new vision of the museum is proposed in which, beginning with the antiquarian and nineteenth-century vision of museum collections, develops into what should be defined as a connected museum or museum of connected narration.