As a cost-effective aerial platform, unmanned aerial vehicles (UAVs) can provide reliable air-to-ground (A2G) line-of-sight (LOS) transmission and controllable maneuverability. However, the LOS links may deteriorate severely in some complex propagation environments, such as in urban areas. In addition, UAV communications often suffer from serious interference caused by the A2G channel. To address these challenges, intelligent reflecting surface (IRS) has been recently proposed to compensate for the path loss and reduce interference. In this article, after briefly introducing the comprehensive background of UAV communications and IRS-based beamforming, the main advantages and the potential of IRS-assisted UAV communications are discussed. Finally, based on a novel active IRS, two case studies are investigated where the transmission beamforming and the active IRS's reflecting coefficient are jointly optimized. In the first case, transmit power of UAVborne base stations can be greatly reduced while ensuring the achievable secure rate. Based on the first case, in the second one, considering the channel error caused by UAV jittering, a robust and secure beamforming was presented. Simulation results are provided to demonstrate the better performance enhancement brought by combining UAVs and active IRSs. Finally, some challenging issues to be resolved for practical implementations were discussed.