Optics has become a major tool for the study of graphene. Indeed the visibility of a single layer was a major factor in the isolation of graphene in the first instance. We will theoretically study optical properties of graphene-based nanostructures over a wide range of frequencies. As a gapless semiconductor with gate-controlled properties graphene is an excellent candidate for terahertz applications. At high frequencies, the peculiar band structure allows linearly-polarised optical transitions to separate particles with different valley quantum numbers in a fashion similar to what optical orientation by circularly polarised light in conventional semiconductors does to spin. In this project, optical and magneto-optical properties of single layer, few-layer graphene, nanoribbons and carbon nanotubes (rolled graphene) will be studied, focusing on their prospective terahertz and valleytronics applications. The studentship will also provide theoretical support to the planned Raman spectroscopy experiments in the Quantum Systems and Nanomaterials group and terahertz experiments performed in the Electromagnetic Materials group within the School.