Fog Radio Access Network (F-RAN) is an emerging wireless network architecture that leverages caching capabilities at the wireless edge nodes, as well as edge connectivity to the cloud via fronthaul links. This paper aims at providing a latency-centric analysis of the degrees of freedom of an F-RAN by accounting for the total content delivery delay across the fronthaul and wireless segments of the network. The main goal of the analysis is the identification of optimal caching, fronthaul and edge transmission policies. The study is based on the introduction of a novel performance metric, referred to as the Normalized Delivery Time (NDT), which measures the total delivery latency as compared to an ideal interference-free system. An information-theoretically optimal characterization of the trade-off between NDT, on the one hand, and fronthaul and caching resources, on the other, is derived for a class of F-RANs with two edge nodes and two users. Using these results, the interplay between caching and cloud connectivity is highlighted, as well as the impact of both caching and fronthaul resources on the delivery latency.