The discovery of Novoselov et al. (2004) of a simple method to transfer a single atomic layer of carbon from the c-face of graphite to a substrate suitable for the measurement of its electrical and optical properties has led to a renewed interest in what was considered to be before that time a prototypical, yet theoretical, two-dimensional system. Indeed, recent theoretical studies of graphene reveal that the linear electronic band dispersion near the Brillouin zone corners gives rise to electrons and holes that propagate as if they were massless fermions and anomalous quantum transport was experimentally observed. Recent calculations and experimental determination of the optical phonons of graphene reveal Kohn anomalies at high-symmetry points in the Brillouin zone. They also show that the Born-Oppenheimer principle breaks down for doped graphene. Since a carbon nanotube can be viewed as a rolled-up sheet of graphene, these recent theoretical and experimental results on graphene should be important to researchers working on carbon nanotubes. The goal of this contribution is to review the exciting news about the electronic and phonon states of graphene and to suggest how these discoveries help understand the properties of carbon nanotubes.