There are two main questions regarding the interaction of drones with wireless networks: first, how wireless networks can support personal or professional use of drones, and second, how drones can support wireless network performance (i.e., boosting capacity on demand, increasing coverage range, enhancing reliability and agility as an aerial node). From a communications perspective, this article categorizes drones in the first case as mobile-enabled drones (MEDs) and drones in the second case as wireless infrastructure drones (WIDs). At the dawn of 5G Release-16, this study investigates both the MED and WID cases within the realistic constraints of 5G. Furthermore, we discuss potential solutions for highlighted open issues, either via application of current standards or by providing suggestions toward further enhancements. Although integrating drones into cellular networks is a rather complicated issue, 4G LTE-A and the 5G Rel-15 standards seem to have significant accomplishments in building fundamental mechanisms. Nevertheless, finetuning future releases by studying existing methods from the aspects of MEDs and WIDs, and bridging the gaps with new techniques are still needed.