This article presents a comprehensive study on the emerging near-space communications (NS-COM) within the context of space-air-ground-sea integrated network (SAGSIN). Specifically, we firstly explore the recent technical developments of NS-COM, followed by the discussions about motivations behind integrating NS-COM into SAGSIN. To further demonstrate the necessity of NS-COM, a comparative analysis between the NS-COM network and other counterparts in SAGSIN is conducted, covering aspects of deployment, coverage, channel characteristics and unique problems of NS-COM network. Afterwards, the technical aspects of NS-COM, including channel modeling, random access, channel estimation, array-based beam management and joint network optimization, are examined in detail. Furthermore, we explore the potential applications of NS-COM, such as structural expansion in SAGSIN communication, civil aviation communication, remote and urgent communication, weather monitoring and carbon neutrality. Finally, some promising research avenues are identified, including stratospheric satellite (StratoSat) -to-ground direct links for mobile terminals, reconfigurable multiple-input multiple-output (MIMO) and holographic MIMO, federated learning in NS-COM networks, maritime communication, electromagnetic spectrum sensing and adversarial game, integrated sensing and communications, StratoSat-based radar detection and imaging, NS-COM assisted enhanced global navigation system, NS-COM assisted intelligent unmanned system and free space optical (FSO) communication. Overall, this paper highlights that the NS-COM plays an indispensable role in the SAGSIN puzzle, providing substantial performance and coverage enhancement to the traditional SAGSIN architecture.