The terahertz frequency band has emerged as a promising candidate for the next generation of satellite communication systems, necessitating thorough investigations into the modeling of space terahertz communication channels. This paper reviews the state-of-the-art in modeling technology for space terahertz communication channels. We commence by outlining the unique propagation characteristics of the terahertz frequency band in space communication systems. Subsequently, we categorize spatial terahertz communication channel models and discuss the crucial factors that must be considered during channel modeling in diverse scenarios. We provide a comprehensive review of the research progress pertaining to each of these factors. Finally, we summarize the current research outcomes and offer insights into potential future research directions, thereby laying the foundation for the integration of terahertz technology into the realm of satellite communications.