High-throughput unmanned aerial vehicle (UAV) communication may unleash the true potential of novel applications for aerial vehicles but also represents a threat for cellular networks due to the high levels of generated interference. In this article, we investigate how a beamforming system installed on board a UAV can be efficiently used to ensure high-throughput uplink UAV communications with minimum impact on the services provided to users on the ground. We study two potential benefits of beamforming, namely, spatial filtering of interference and load balancing, considering different beam switching methodologies. Our analysis is based on system-level simulations followed by a series of measurement campaigns in live Long-Term Evolution (LTE) networks. Our results show that using UAV-side beamforming has a great potential to increase uplink throughput of a UAV while mitigating interference. When beamforming is used, even up to twice as many UAVs may be served within a network compared with UAVs using omni-directional antennas, assuming a constant uplink throughput target. However, to fully exploit the potential of beamforming, a standardized solution ensuring alignment between network operators and UAV manufacturers is required.