The forthcoming sixth generation (6G) communication network is envisioned to provide ultra-fast data transmission and ubiquitous wireless connectivity. The terahertz (THz) spectrum, with higher frequency and wider bandwidth, offers great potential for 6G wireless technologies. However, the THz links suffers from high loss and line-of-sight connectivity. To overcome these challenges, a cost-effective method to dynamically optimize the transmission path using reconfigurable intelligent surfaces (RISs) is widely proposed. RIS is constructed by embedding active elements into passive metasurfaces, which is an artificially designed periodic structure. However, the active elements (e.g., PIN diodes) used for 5G RIS are impractical for 6G RIS due to the cutoff frequency limitation and higher loss at THz frequencies. As such, various tuning elements have been explored to fill this THz gap between radio waves and infrared light. The focus of this review is on THz RISs with the potential to assist 6G communication functionalities including pixel-level amplitude modulation and dynamic beam manipulation. By reviewing a wide range of tuning mechanisms, including electronic approaches (complementary metal-oxide-semiconductor (CMOS) transistors, Schottky diodes, high electron mobility transistors (HEMTs), and graphene), optical approaches (photoactive semiconductor materials), phase-change materials (vanadium dioxide, chalcogenides, and liquid crystals), as well as microelectromechanical systems (MEMS), this review summarizes recent developments in THz RISs in support of 6G communication links and discusses future research directions in this field.