Future generations of wireless networks are expected to provide new services with an unprecedented level of diverse and stringent requirements. Fog Radio Access Network (FRAN) and Non-Orthogonal Multiple Access (NOMA) have emerged as complimentary enablers to meet such requirements. On the one hand, FRAN architecture is designed to reduce the delay caused by the fronthaul link by pushing control and storage to the network edge. On the other hand, in addition to increasing the spectral and energy efficiency and the number of connected devices, NOMA has the potential to improve network latency. This paper overviews the joint benefits of enabling NOMA schemes in an FRAN architecture, by means of examining the applicability and adequateness of the NOMA-based FRAN features in achieving specific objectives of next generation of mobile networks, mainly those related to enhanced mobile broadband (eMBB), massive machine type communications (mMTC), and ultra-reliable low latency communication (URLLC). The paper further depicts the challenges and future research directions that must be addressed in order to meet such opportunities. This work was funded in part by King Abdullah University of Science and Technology (KAUST) and by the Grant-in-Aid for Scientific Research (Kakenhi) no. 17K06453 from the Ministry of Education, Science, Sports, and Culture of Japan and the NII MoU grants, and in part by the Center of Excellence for NEOM Research at KAUST.