In this review paper we explore different antenna technologies at terahertz frequencies for space science and other applications. We show that the antenna technologies generally used at lower frequencies are difficult to implement at terahertz frequencies. Additionally, one has to take a few extra steps and special care for designing antennas for space-based applications. In this paper, we review different design and implementation options for millimeter-wave and terahertz antennas for space applications. We detail how antenna design has to be a part of the overall system design for the success of the instruments for space missions. We also look into low-mass and low-profile conformal antenna technologies that will have a profound impact on future space instruments at terahertz frequencies.