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Resumen del trabajo presentado al Workshop on Graphene, celebrado en el Donostia International Physics Center (DIPC) del 29 de agosto al 2 de septiembre de 2011,San Sebastián, Spain., Recently, it was shown that polarization of a two-dimensional graphene sheet by an external charge produces an attractive image potential that supports, in addition to the wellknown π* bands, a double series of Rydberg-like image potential states converging onto the vacuum level. Being quantified in the direction perpendicular to the graphene sheet, in the parallel plane these states have nearly free electron character, like similar states on metal surfaces. A large extension of wave function of image-potential states into the vacuum implies that they are very sensitive to any change of shape and environment of the graphene sheet. Thus, the properties of these states can be modified by an external electric field and a shape/geometry variation. The lowest-energy members of such states have been experimentally observed in graphene sheets grown on some substrates. Some examples of such unoccupied electronic states in other carbon-based materials, like graphite, multilayer graphene, fullerenes, and nanotubes as having common origin with the graphene image-potential states will be presented.