Enabling high-rate, low-latency and ultra-reliable wireless communications between unmanned aerial vehicles (UAVs) and their associated ground pilots/users is of paramount importance to realize their large-scale usage in the future. To achieve this goal, cellular-connected UAV, whereby UAVs for various applications are integrated into the cellular network as new aerial users, is a promising technology that has drawn significant attention recently. Compared to the conventional cellular communication with terrestrial users, cellular-connected UAV communication possesses substantially different characteristics that bring in new research challenges as well as opportunities. In this article, we provide an overview of this emerging technology, by firstly discussing its potential benefits, unique communication and spectrum requirements, as well as new design considerations. We then introduce promising technologies to enable the future generation of three-dimensional (3D) heterogeneous wireless networks with coexisting aerial and ground users. Last, we present simulation results to corroborate our discussions and highlight key directions for future research.