Non-orthogonal multiple access (NOMA) enabled fog radio access networks (NOMA-F-RANs) have been taken as a promising enabler to release network congestion, reduce delivery latency, and improve fog user equipments' (F-UEs') quality of services (QoS). Nevertheless, the effectiveness of NOMA-F-RANs highly relies on the charted feature information (preference distribution, positions, mobilities, etc.) of F-UEs as well as the effective caching, computing, and resource allocation strategies. In this article, we explore how artificial intelligence (AI) techniques are utilized to solve foregoing tremendous challenges. Specifically, we first elaborate on the NOMA-F-RANs architecture, shedding light on the key modules, namely, cooperative caching and cache-aided mobile edge computing (MEC). Then, the potentially applicable AI-driven techniques in solving the principal issues of NOMA-F-RANs are reviewed. Through case studies, we show the efficacy of AI-enabled methods in terms of F-UEs' latent feature extraction and cooperative caching. Finally, future trends of AI-driven NOMA-F-RANs, including open research issues and challenges, are identified.