Low-altitude unmanned aerial vehicles (UAVs), a.k.a. drones, have enabled a plethora of personal and commercial applications including aerial photography and sightseeing, parcel delivery, search-and-rescue, monitoring and surveillance, and precision farming. Improving the operation range and safety of the drones has led to increasing interest in connecting drones over licensed spectrum as three-dimensional (3D) aerial users and employing the fifth-generation (5G) cellular infrastructure for reliable beyond-visual-line-of-sight communication and control. On the other hand, drones with flexible mobility and large payload also enable aerial base stations (BSs) to establish, enhance, and recover cellular coverage in real-time for ground users in remote, densely populated, and disastrous areas, unlocking an unprecedented opportunity for intelligent cellular network operation in both normal and emergent scenarios. To address the socioeconomic impact of emerging aerial users and aerial BSs, this project will study cellular-connected drones in 5G and beyond via (i) assessing the applicability of 5G new radio (NR) technologies and the required enhancements towards reliable, long-range, and efficient drone communication and control, (ii) resolving key challenges for drone communication and control through novel hardware (such as antenna design and deployment) and software (including communication protocols, control schemes, signal processing algorithms, and network architectures) designs, (iii) investigating the impact of 3D mobile drones and necessary changes on 5G terrestrial communication, signal processing, resource allocation and networking, and (iv) testing drone communication and control with practical experimentation setups and in real national 5G testbeds.