As an emerging vertical heterogeneous network architecture that integrates the satellite-based space networks, air networks, and traditional ground networks, space–air–ground integrated network (SAGIN) is developed to realize the Internet of everything, global coverage, and ubiquitous intelligent communications. However, SAGIN also faces quite a few challenges due to its unique characteristics, such as highly complex network architecture, highly dynamic node topology, time-varying communication channels, and restricted resources. In this paper, we first introduce the architecture and benefits of SAGIN, and then present the faced challenges. Next, we discuss some key technologies in SAGIN. In particular, we discuss the flexible access in the realization of a dynamic communication architecture, explore some efficient resource scheduling methods to avoid wastage of resources, and investigate the secure communications, such as covert communications, physical layer security, and anti-jamming communications, in SAGIN. Finally, the potential future directions are discussed.