The growing use of Unmanned Aerial Vehicles (UAVs) for various applications requires ubiquitous and reliable connectivity for safe control and data exchange between these devices and ground terminals. Depending on the application, UAV-mounted wireless equipment can either be an aerial user equipment (AUE) that co-exists with the terrestrial users, or it can be a part of wireless infrastructure providing a range of services to the ground users. For instance, AUE can be used for real-time search and rescue and Aerial Base Station (ABS) can enhance coverage, capacity, and energy efficiency of wireless networks. We will start with discussing the open challenges of communication with UAVs. To give answers to the posed questions, we will focus on the UAV communication basics, providing the channel modeling background and giving guidelines on how various channel models should be used. Next, theoretical, simulation- and measurement-based approaches to address the key challenges for AUE usage will be presented. Moreover, we will provide a comprehensive overview on how UAV-mounted equipment (e.g. ABS) can be used as a part of the communication network. Based on the theoretical analysis, we will show how various network parameters (for example coverage area of ABSs, power efficiency, or user localization error) can be optimized. Finally, we will discuss how to ensure the safe use of UAVs via various RF-based techniques for detecting the presence of UAVs in the airspace (including Machine Learning and Passive Coherent Location techniques).