Abstract: Graphene is a very promising rising star in material science and physics. As an excellent two-dimensional material with high crystal and electronic qualities, Graphene exhibits unique electron transport, optical coupling, magnetic and other properties. For example, Graphene has zero bandgap and zero effective mass, with electrons and holes behaving as relativistic particles. Moreover, Graphene has the highest mobility which is almost independent of temperature. Among a cornucopia of new physics and potential applications, Graphene has intriguing uses in terahertz (THz) science because it is closely related to THz waves through plasma oscillation, externally tunable resistivity, and variable THz bandgaps. In this paper an introduction to Graphene and its recent progress is given. The prospects of Graphene in THz science are discussed, including its THz properties and device potential.