Autonomous Industrial Cyber-Physical Systems (ICPS) represent a future vision where industrial systems achieve full autonomy, integrating physical processes seamlessly with communication, computing and control technologies while holistically embedding intelligence. Cloud-Fog Automation is a new digitalized industrial automation reference architecture that has been recently proposed. This architecture is a fundamental paradigm shift from the traditional International Society of Automation (ISA)-95 model to accelerate the convergence and synergy of communication, computing, and control towards a fully autonomous ICPS. With the deployment of new wireless technologies to enable almost-deterministic ultra-reliable low-latency communications, a joint design of optimal control and computing has become increasingly important in modern ICPS. It is also imperative that system-wide cyber-physical security are critically enforced. Despite recent advancements in the field, there are still significant research gaps and open technical challenges. Therefore, a deliberate rethink in co-designing and synergizing communications, computing, and control (which we term “3C co-design”) is required. In this paper, we position Cloud-Fog Automation with 3C co-design as the new paradigm to realize the vision of autonomous ICPS. We articulate the state-of-the-art and future directions in the field, and specifically discuss how goal-oriented communication, virtualization-empowered computing, and Quality of Service (QoS)-aware control can drive Cloud-Fog Automation towards a fully autonomous ICPS, while accounting for system-wide cyber-physical security.