Terahertz (THz) band will play an important role in enabling sixth generation (6G) envisioned applications. Compared with lower frequency signals, THz waves are severely attenuated by the atmosphere temperature, pressure, and humidity. Thus, designing a THz communication system must take into account how to circumvent or diminish those issues to achieve a sufficient quality of service. Different solutions are being analyzed: intelligent communication environments, ubiquitous artificial intelligence, extensive network automation, and dynamic spectrum access, among others. This survey focuses on the benefits of integrating intelligent surfaces (ISs) and THz communication systems by providing an overview of IS in wireless communications with the scanning of the recent developments, a description of the architecture, and an explanation of the operation. The survey also covers THz channel models, differentiating them based on deterministic and statistical channel modeling. The IS-aided THz channels are elucidated at the end of the survey. Finally, discussions and research directions are given to help enrich the IS field of research and guide the reader through open issues.