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Given the explosive growth of Internet of Things (IoT) devices ranging from the two-dimensional (2D) ground to the three-dimensional (3D) space, it is a necessity to establish a 3D spectrum map to comprehensively present and effectively manage the 3D spatial spectrum resources in smart city infrastructures. By leveraging the popularity and location flexibility of the unmanned aerial vehicles (UAVs), we are able to execute spatial sampling with these emerging flying spectrum-monitoring devices (SMDs) at will. In this paper, we first present a brief survey to show the state-of-the-art studies on spectrum mapping. Then, we introduce the 3D spectrum mapping model. Next, we propose a 3D spectrum mapping framework which is composed of pre-sampling, spectrum situation estimation, UAV deployment and spectrum recovery. Therein we develop a Region of Interest (ROI)-driven UAV deployment scheme, which selects new sampling points of the highest estimated interest and the lowest energy cost iteratively. Meanwhile, we slice the entire 3D spectrum map into a series of "images" and "repair" those unsampled locations. Furthermore, we provide an exemplary case study on the 3D spectrum mapping, where, for example, an important event is being held and the entire spectrum situation needs to be monitored in real time to deal with malicious interference sources. Lastly, the challenges and open issues are discussed.