Quantum communication is an innovative method of transmitting information that utilizes quantum states. It encompasses research areas such as quantum key distribution and quantum secure direct communication. By harnessing the properties of quantum mechanics, quantum communication enables theoretically absolute secure transmission that is immune to eavesdropping or decryption through computational means. The terahertz band, well-known for its high frequency and wide bandwidth capabilities, has emerged as the preferred frequency range for 6th Generation (6G) wireless communication. Therefore, the combination of terahertz communication with quantum communication holds great potential for enhancing secure communication in the era of 6G. This article offers a comprehensive overview of the advancements in terahertz quantum communication for the first time, with a specific focus on the latest research progress of terahertz quantum key distribution in terrestrial atmospheric environments and inter-satellite link.