The interplay between artificial in-telligence (AI) and fog radio access networks (F-RANs) is investigated in this work from two perspectives: how F-RANs enable hierar-chical AI to be deployed in wireless networks and how AI makes F-RANs smarter to better serve mobile devices. Due to the heterogeneity of processing capability, the cloud, fog, and device layers in F-RANs provide hierarchical intelligence via centralized, distributed, and federated leing. In addition, cross-layer leing is also introduced to further reduce the demand for the memory size of the mo-bile devices. On the other hand, AI provides F-RANs with technologies and methods to deal with massive data and make smarter de-cisions. Specifically, machine leing tools such as deep neural networks are introduced for data processing, while reinforcement leing (RL) algorithms are adopted for net-work optimization and decisions. Then, two examples of AI-based applications in F-RANs, i.e., health monitoring and intelligent transpor-tation systems, are presented, followed by a case study of an RL-based caching application in the presence of spatio-temporal unknown content popularity to showcase the potential of applying AI to F-RANs.