The electronic structure and the quantum transport properties of graphene, carbon nanotubes and graphene nanoribbons are studied using analytical and numerical tools, taking special care in considering fundamental questions of high experimental relevance and in relating the results to experiments. Based on the tight-binding description of electrons and integrating the results of microscopic ab initio calculations as well as several minimal models at various degrees of detail, the Landauer formalism of linear conductance is applied in combination with Green function decimation algorithms for...