The paper reviews author’s recent theoretical works on the carbon nanostructures including fullerenes and nanotubes. The developments of the ab initio method using the localized basis set are also described with an introduction to the requirement for large-sized first-principles calculations. The total energy calculations on the sp2-bonded carbon structures show that the energetics regarding the incorporation of pentagonal rings favors the curvature of the C240 and, consequently, the cap of the (10,10) nanotube. As a study aiming at a practical application, field emission properties of the carbon nanotube are investigated. A general introduction to the various advantages of the carbon nanotube as an electron field emitter is followed by detailed studies on the oxygen adsorption effects.