Unmanned aerial vehicles (UAVs) provide flexible wireless access to future wireless networks and have wider coverage with higher transmission rates. However, because the wireless backhaul for UAVs is usually capacity limited and congested, and, because UAVs cannot operate for long periods of time due to their limited battery life, we propose a framework of caching UAV-enabled smallcell networks to offload the data traffic of small-cell base stations (SBSs). In the proposed scheme, the most common content is stored in local caches of UAVs in advance and delivered to mobile users directly from the caches when required. Thus, the wireless backhaul congestion can be alleviated, the energy consumption can be reduced, and the quality of experience (QoE) can be improved. Based on this framework, typical schemes of caching UAV-enabled small-cell networks are demonstrated, and the distributed caching strategy for UAVs is discussed. For illustration, a case study of interference management is also presented. Finally, several interesting research issues and challenges are discussed for caching UAVenabled networking.