It has become increasingly apparent that the future of next generation of electronic devices can and will rely on graphene nanoribbons. Graphene nanoribbons and sister structures showcase several key properties that can address the emerging need of terahertz science and technology, and break through the many technological limits on conventional semiconductor electronics operating in the terahertz spectrum. In this thesis, we focus on the study of the terahertz nonlinear optical response of metallic armchair graphene nanoribbons and sister structures using a k.p model and time dependent perturbation theory. We find that these nanoribbons exhibit a stronger interband optical response, and a smaller critical field strength (of the order of 10 kV/m) than does 2D single layer graphene. We demonstrate that finite ribbon size, spatial profile of the applied terahertz radiation field, polarization of the applied terahertz radiation, a small band gap opening, and application of a superlattice potential are several ways to tune the strong terahertz nonlinear optical response of metallic armchair graphene nanoribbons. The major contributions of this thesis include: 1) developes of a simpler method compared to other sophisticated methods of the terahertz nonlinear optical interband response of metallic armchair graphene nanoribbons; 2) extends the method in the characterization of various quantum size effects, elliptically polarized radiation field, small gap opening and superlattice on the terahertz optical response of these nanoribbons; 3) The versatility of the tunability showed in the terahertz nonlinear response of metallic armchair nanoribbons and sister structures will help advance the development of the nonlinear terahertz armchair graphene nanoribbon opto-electronic and photonic technology.