The optical properties of graphene-based nanomaterials have attracted much recent attention. This article provides an overview of recent advances in the study of linear and nonlinear optical transitions associated mostly with tailored energy bandgaps. In particular, the optical absorption characteristics and photoluminescence emissions due to various induced bandgaps and, in some cases, the formation of graphene quantum dots are highlighted. Nonlinear optical properties of these materials are reviewed with an emphasis on optical limiting through both nonlinear absorption and scattering mechanisms.
