Carbon nanostructures offer exciting new possibilities in the detection of light dark matter. A dark matter particle with mass between 1 MeV and 1 GeV scattering off an electron in the carbon would transfer sufficient energy to extract the electron from the lattice. In 2D materials, such as graphene or carbon nanotubes, these electrons would be released directly into the vacuum, avoiding their re-absorption in the medium. We present two novel detector concepts: a 'Graphene-FET' design, based on graphene sheets, developed at Princeton University; and a 'Dark-PMT' based on aligned carbon nanotubes, developed in University of Rome Sapienza. We discuss their light dark matter discovery potential, the status of the R&D, and the recent commissioning of a state-of-the-art carbon nanotube growing facility in Rome.