In the last few years, unmanned aerial vehicles (UAVs) have been standing out as a pervasive tool in numerous civil and commercial applications. Although different wireless technologies can be employed to establish communications between a UAV and a ground control station (GCS), most either limit the operational radius or increase substantially the complexity of the system. Taking into account insights from our own real-world experiments and studies carried out within the scope of the SAAS project from Instituto de Telecomunicações, in this article we discuss the use of mobile networks for low altitude air-to-ground (A2G) communications as a possible solution to provide extended mobility and range to operators and UAVs. Besides addressing the advantages and the associated constraints of using these networks, we propose a flexible architecture for multiple UAVs and GCSs. Although our experimental results have shown that current mobile networks can fulfil the basic requirements for many envisioned UAV applications, we discuss how the evolution towards 5G networks is expected to improve the support for reliable real-time A2G communications and even for air-to-air communications.