Precision health, increasingly supported by digital technologies, is a domain of research that broadens the paradigm of precision medicine, advancing everyday healthcare. This vision goes hand in hand with the groundbreaking advent of artificial intelligence (AI), which is reshaping the way we diagnose, treat, and monitor both clinical subjects and the general population. AI tools powered by machine learning have shown considerable improvements in a variety of healthcare domains. In particular, reinforcement learning (RL) holds great promise for sequential and dynamic problems such as dynamic treatment regimes and just-in-time adaptive interventions in digital health. In this work, we discuss the opportunity offered by AI, more specifically RL, to current trends in healthcare, providing a methodological survey of RL methods in the context of precision and digital health. Focusing on the area of adaptive interventions, we expand the methodological survey with illustrative case studies that used RL in real practice. This invited article has undergone anonymous review and is intended as a book chapter for the volume "Frontiers of Statistics and Data Science" edited by Subhashis Ghoshal and Anindya Roy for the International Indian Statistical Association Series on Statistics and Data Science, published by Springer. It covers the material from a short course titled "Artificial Intelligence in Precision and Digital Health" taught by the author Bibhas Chakraborty at the IISA 2022 Conference, December 26-30 2022, at the Indian Institute of Science, Bengaluru.