Precipitated by the technological innovations of the near-space platform stations (NSPS), the near space communication (NS-COM) network has emerged as an indispensable part of the next-generation space-air-ground integrated network (SAGIN) that facilitates ubiquitous coverage and broadband data transfer. This paper aims to provide a comprehensive overview of NS-COM. Firstly, we investigate the differences between NS-COM and the existing terrestrial cellular networks as well as satellite-based and unmanned-aerial-vehicle (UAV)-based communication networks, which is followed by a review of the NS-COM development. Then, we explore the unique characteristics of NS-COM regarding the platforms and the propagation environment of the near space. The main issues of NS-COM are identified, resulted from the extremely long transmission distance, limitations of the communication payloads on NSPS and complex atmospheric constitution of the near space. Then various application scenarios of NS-COM are discussed, where the special technical requirements are also revealed, from the physical-layer aspect like transceiver design to the upper-layer aspect like computational offloading and NSPS placement. Furthermore, we investigate the co-existence of NS-COM and ground networks by treating each other as interferers or collaborators. Finally, we list several potential technologies for NS-COM from the perspective of spectrum usage, and highlight their technical challenges for future research.