The utilization of terahertz (THz) band in the electromagnetic spectrum has great potential value both in scientific research and practical applications, therefore reasonable design of antenna system for radiating and receiving THz wave is especially critical. This article reviews the THz antenna technology toward atmospheric remote sensing, radio astronomy, and deep space exploration over the past three decades. Some typical scientific and engineering applications in space are discussed, which include the specifications, design issues, and the performance of various space THz antenna systems. Horn array antennas (synthetic aperture radiometry), reflector antennas fed by quasi-optical networks and traditional microwave networks have been widely applied in the designs for science missions. Finally, some promising THz antennas for future missions are introduced, and viewpoints on research challenges and future directions are given.