Graphene plasmons are rapidly emerging as a viable tool for fast electrical manipulation of light. The prospects for applications to electro-optical modulation, optical sensing, quantum plasmonics, light harvesting, spectral photometry, and tunable lighting at the nanoscale are further stimulated by the relatively low level of losses and high degree of spatial confinement that characterize these excitations compared with conventional plasmonic materials. We start with a general description of the plasmons in extended graphene, followed by analytical methods that lead to reasonably accurate estimates of both the plasmon energies and the strengths of coupling to external light in graphene nanostructures, including graphene ribbons. We discuss several possible strategies to extend these plasmons towards the visible and near infrared, including a reduction in the size of the graphene structures and an increase in the level of doping. Specifically, we discuss plasmons in narrow ribbons and molecular-size graphene structures. We further formulate prescriptions based on geometry to increase the level of electrostatic doping without causing electrical breakdown. Results are also presented for plasmons in highly-doped single-wall carbon nanotubes, which exhibit similar characteristics as narrow ribbons and show a relatively small dependence on the chirality of the tubes. We further discuss perfect light absorption by a single-atom carbon layer, which we illustrate by investigating arrays of ribbons using fully analytical expressions. Finally, we explore the possibility of exploiting optically pumped transient plasmons in graphene, whereby the optically heated graphene valence band can sustain collective plasmon oscillations similar to those of highly doped graphene, and well-defined during the picosecond time window over which the electron is at an elevated temperature.