As mobile data traffic keeps growing and mobile applications pose increasingly stringent and diverse requirements, wireless networks are facing unprecedented pressures. Network infrastructure densification presents promises to further evolve wireless networks and maintain their competitiveness. Deploying more radio access points equipped with storage and computation capabilities can increase network capacity, improve network energy efficiency, provide low-latency services and access for massive devices. The benefits of network densification can be exploited using the emerging fog radio access network (Fog-RAN) architecture by pushing computation and storage resources to network edges. However, it comes with formidable technical challenges. Innovative methodologies are needed to operate such networks with various resources. This chapter develops a generalized low-rank optimization model for performance enhancements in ultra-dense Fog-RANs, supported by various motivating design objectives including mobile edge caching and topological interference alignment. A special attention is paid on algorithmic approaches for nonconvex low-rank optimization problems via Riemannian optimization.