To achieve ubiquitous connectivity in next-generation networks through aerospace communications while maintaining high data rates, Terahertz (THz) band communications (0.1-10 THz) with large continuous bandwidths are considered a promising candidate technology. However, key enabling techniques and practical implementations of THz communications for aerospace applications remain limited. In this paper, the wireless channel characteristics, enabling communication techniques, and networking strategies for THz aerospace communications are investigated, aiming to assess their feasibility and encourage future research efforts toward system realization. Specifically, the wireless channel characteristics across various altitudes and scenarios are first analyzed, focusing on modeling the interaction between the THz wave and the external environment, from ground to outer space. Next, key enabling communication technologies, including multiple-input multiple-output (MIMO) technique, beam alignment and tracking, integrated communication and radar sensing (ICARS), and resource allocation for networking are discussed. Finally, the existing challenges and possible future directions are summarized and discussed.