Due to their high maneuverability, flexible deployment, and low cost, unmanned aerial vehicles (UAVs) are expected to play a pivotal role in not only communication, but also sensing. Especially by exploiting the ultra-wide bandwidth of terahertz (THz) bands, integrated sensing and communication (ISAC)-empowered UAV has been a promising technology of 6G space-air-ground integrated networks. In this article, we systematically investigate the key techniques and essential obstacles for THz-ISAC-empowered UAV from a transceiver design perspective, with the highlight of its major challenges and key technologies. Specifically, we discuss the THz-ISAC-UAV wireless propagation environment, based on which several channel characteristics for communication and sensing are revealed. We point out the transceiver payload design peculiarities for THz-ISAC-UAV from the perspective of antenna design, radio frequency front-end, and baseband signal processing. To deal with the specificities faced by the payload, we shed light on three key technologies, i.e., hybrid beamforming for ultra-massive MIMO-ISAC, power-efficient THz-ISAC waveform design, as well as communication and sensing channel state information acquisition, and extensively elaborate their concepts and key issues. More importantly, future research directions and associated open problems are presented, which may unleash the full potential of THz-ISAC-UAV for 6G wireless networks.