The use of unmanned aerial vehicles (UAV) as flying radio access network (RAN) nodes offers a promising complement to traditional fixed terrestrial deployments. More recently yet still in the context of wireless networks, drones have also been envisioned for use as radio frequency (RF) sensing and localization devices. In both cases, the advantage of using UAVs lies in their ability to navigate themselves freely in 3D and in a timely manner to locations of space where the obtained network throughput or sensing performance is optimal. In practice, the selection of a proper location or trajectory for the UAV very much depends on local terrain features, including the position of surrounding radio obstacles. Hence, the robot must be able to map the features of its radio environment as it performs its data communication or sensing services. The challenges related to this task, referred here as radio mapping, are discussed in this paper. Its promises related to efficient trajectory design for autonomous radio-aware UAVs are highlighted, along with algorithm solutions. The advantages induced by radio-mapping in terms of connectivity, sensing, and localization performance are illustrated.