Abstract: Graphene-based field effect transistors (GFETs) have a higher charge mobility and a higher cut-off frequency than traditional silicon-based transistors and are also smaller. The symmetrical conical band structure of the graphene channel with no band gap and negative dynamic conductivity of graphene with optical pumping in the terahertz (THz) band make them widely applicable in THz function devices, which are low cost and compatible with current semiconductor technology. In this paper, the scaling challenges for silicon-based transistors are discussed, and the basic structure, fabrication process and the main characteristics (C-V and I-V) in the THz/RF region for GFETs and graphene nanoribbon FETs are reviewed. Their novel uses in terahertz technology such as a terahertz electronic injection laser, a FET terahertz detector, a broadband FET terahertz modulator and an oscillator are summarized.