The purpose of this chapter is to describe and review examples of how theoretical investigations can be applied to elucidate the behavior of carbon nanostructures and to understand the physical mechanisms taking place at the molecular level. We will place a special emphasis in theoretical works utilizing density functional theory. We assume that the reader is familiar with the basics of density functional theory as well as the electronic properties of single-walled carbon nanotubes and graphene nanoribbons (GNRs). We do not intend to present an extensive review; instead, we focus on several examples to illustrate the powerful predictive capabilities of current computational approaches.