among the low–dimensional allotropes of carbon, nanotubes and graphene have attracted very much attention from nano–science and nanotechnology specialists. they have been proposed as building blocks in nanometer device engineering. however, these structures are not defect–free. in this thesis, we focused on defective carbon nanotubes and graphene, and studied the effect of couple of very commonly occurring defects, namely a short–range defect (point–like), a long–range defect (ripple), and a 5–7 stone–wales defect. the methods used for obtaining the electronic properties were mainly based on tight–binding (tb) model, and density–functional theory (dft). moreover, we used a unique approach to density–functional calculations based on order–n methods, in which the computational cost scales linearly with the system size. based on landauer–bu ?ttiker formalism, we showed that the first correction term to the quantum conductance of the system was dependent on the place where the defect was situated. as such, measuring the fluctuations of the conductance from its expected value in perfect samples, we can map out the under–lying structure of the system. this could be used as a new imaging method. we also addressed the widely debated controversy of ripples on the surface of graphene. we showed that the ripples were indeed an intrinsic property of graphene membranes in finite temperatures and they would be present whether the substrate was present or not. we also showed that there was a relatively strong correlation between the charge inhomogeneity on the surface and the local structural features. the effect of different orientations of stone–wales defects on generally metallic armchair carbon nanotubes was also investigated using linear–scaling density–functional theory calculations. there are two possible orientations for stone–wales defects in achiral (armchair and zigzag) ones. type i defect, lying along the tube axis, induced no gap around the fermi energy of an armchair tube. however, type ii defect, which lied across the circumference, opened a relatively large semiconducting band gap. it was also shown that the vicinity of the type i defect was electron–deficient but that around type ii was electron–rich.