Unmanned aerial vehicles (UAVs) are powerful Internet-of-Things components to provide sensing and communications in the air due to their advantages in mobility and flexibility. As aerial users, UAVs are envisioned to support various sensing applications in the next generation cellular systems, which have been studied by the Third Generation Partnership Project (3GPP). However, the Quality-of-Services (QoS) of the cellular link between the UAV and the base station may not be guaranteed when UAVs are at the cell edge or experiencing deep fading. In this article, we first introduce the non-cooperative cellular Internet of UAVs. Then we propose a cooperative sense-and-send protocol, in which a UAV can upload sensory data with the help of a UAV relay, to provide a better communication QoS for the sensing tasks. Key techniques including trajectory design and radio resource management that support the cooperative cellular Internet of UAVs are presented in detail. Finally, the extended cooperative cellular Internet of UAVs is discussed for QoS improvement with some open issues, such as massive multiple-input multiple-output systems, millimeter-wave, and cognitive communications.