This article reviews the electronic and transport properties of carbon nanotubes. The focus is mainly theoretical, but when appropriate the relation with experimental results is mentioned. While simple band-folding arguments will be invoked to rationalize how the metallic or semiconducting character of nanotubes is inferred from their topological structure, more sophisticated tight-binding and ab initio treatments will be introduced to discuss more subtle physical effects, such as those induced by curvature, tube-tube interactions, or topological defects. The same approach will be followed for transport properties. The fundamental aspects of conduction regimes and transport length scales will be presented using simple models of disorder, with the derivation of a few analytic results concerning specific situations of short- and long-range static perturbations. Further, the latest developments in semiempirical or ab initio simulations aimed at exploring the effect of realistic static scatterers (chemical impurities, adsorbed molecules, etc.) or inelastic electron-phonon interactions will be emphasized. Finally, specific issues, going beyond the noninteracting electron model, will be addressed, including excitonic effects in optical experiments, the Coulomb-blockade regime, and the Luttinger liquid, charge density waves, or superconducting transition.

Hybridization of the ${\mathrm{\sigma }}^{\mathrm{*}}$ and ${\mathrm{\pi }}^{\mathrm{*}}$ states of the graphene network is shown to be as important as band-folding effects in determining the metallicity of small radius carbon nanotubes. Using detailed plane-wave ab initio pseudopotential local density functional (LDA) calculations, we find that the electronic properties of small tubes are significantly altered from those obtained in previous tight-binding calculations. Strongly modified low-lying conduction band states are introduced into the band gap of insulating tubes because of strong ${\mathrm{\sigma }}^{\mathrm{*}\mathrm{-}}$ ${\mathrm{\pi }}^{\mathrm{*}}$ hybridization. As a result, the LDA gaps of some tubes are lowered by more than 50%, and a tube previously predicted to be semiconducting is shown to be metallic.

The quasiparticle band structure of bulk hexagonal boron nitride is studied within the GW approximation for the self-energy operator. The influence of the interlayer distance on the band structure is investigated both within the local density approximation and the quasiparticle approach, and the importance of an interlayer state in determining the gap is demonstrated. Also, the quasiparticle band structure for an isolated sheet of boron nitride is calculated. We show that the equivalent of the interlayer state in the case of the isolated boron nitride sheet plays the same role as in the bulk case in determing the band gap.