Experiential artificial intelligence (AI) is an approach to the design, use, and evaluation of AI in cultural or other real-world settings that foregrounds human experience and context. It combines arts and engineering to support rich and intuitive modes of model interpretation and interaction, making AI tangible and explicit. The ambition is to enable significant cultural works and make AI systems more understandable to nonexperts, thereby strengthening the basis for responsible deployment. This paper discusses limitations and promising directions in explainable AI, contributions the arts offer to enhance and go beyond explainability and methodology to support, deepen, and extend those contributions.