Artificial intelligence (AI) is a game changer in many fields, including cultural heritage. It supports the planning and preservation of heritage sites and cities, enables the creation of virtual experiences to enrich cultural tourism and engagement, supports research, and increases access and understanding of heritage objects. Despite some impressive examples, the full potential of AI for economic, social, and cultural change is not yet fully visible. Against this background, this article aims to (a) highlight the scope of AI in the field of cultural heritage and innovation, (b) highlight the state of the art of AI technologies for cultural heritage, (c) highlight challenges and opportunities, and (d) outline an agenda for AI, cultural heritage, and innovation.