Thanks to their outstanding electrical, mechanical and thermal properties, research in carbon-based materials is one of the most rapidly advancing fronts ever. In this work, we study the effects a time-periodic potential induces on the electronic structure and transport properties in graphene and carbon nanotubes. By combining Floquet theory with Green's function formalism, we describe two different situations: (1) the generation of laser-induced band gaps in graphene and (2) the enhancement of the pumped current in carbon nanotubes. For the first case, we show how the band gaps can be tuned by using the laser polarization and describe a strong suppression in the conductance. For the second case, we observe an enhancement of the pumped current by up to two orders of magnitude when gating the system close to a van Hove singularity (vHs).