Autonomic computing investigates how systems can achieve (user) specified "control" outcomes on their own, without the intervention of a human operator. Autonomic computing fundamentals have been substantially influenced by those of control theory for closed and open-loop systems. In practice, complex systems may exhibit a number of concurrent and inter-dependent control loops. Despite research into autonomic models for managing computer resources, ranging from individual resources (e.g., web servers) to a resource ensemble (e.g., multiple resources within a data center), research into integrating Artificial Intelligence (AI) and Machine Learning (ML) to improve resource autonomy and performance at scale continues to be a fundamental challenge. The integration of AI/ML to achieve such autonomic and self-management of systems can be achieved at different levels of granularity, from full to human-in-the-loop automation. In this article, leading academics, researchers, practitioners, engineers, and scientists in the fields of cloud computing, AI/ML, and quantum computing join to discuss current research and potential future directions for these fields. Further, we discuss challenges and opportunities for leveraging AI and ML in next generation computing for emerging computing paradigms, including cloud, fog, edge, serverless and quantum computing environments.