In this dissertation, statics and dynamics of defects in fullerenes and carbon nanotubes are studied by various computational model, such as ab initio (DFT, semi-empirical, empirical potential) and several computational methods, such as structure relaxation, molecular dynamics and Monte Carlo simulation. Our investigation shows ozone molecule could etch carbon nanotube by forming a precursor, ester-like structure. Molecular dynamics simulation result presents carbon atoms on tube wall was etched away as CO(gas), which is in good agreement with experimental observation. A specific topological defect, pentagon-heptagon pair, an edge dislocation core in hexagonal lattice, is also studied by dislocation theory with atomistic computer simulations. It is shown how the glide of pentagon-heptagon defects and a particular pseudoclimb, with the atoms directly breaking out of the lattice, work concurrently to maintain the tube perfection. Another type of movement of pentagon-heptagon pair, glide involving 90° bond flipping is also studied. Derived force diagram quantifies the balance between these mechanisms, while simulations show both helical and longitudinal movement of the kinks, in agreement with the forces and with experimental observations. Our theoretical modeling also indicates that pentagons play a critical role in giant fullerene sublimation. Carbon atoms are removed predominantly from the weakest binding energy sites, i.e., the pentagons, leading to the constant evaporation rate. The fullerene cage integrity is attributed to the collective behavior of interacting defects. We also examine the formation and dynamics of edge dislocation in carbon nanotubes theoretically. Our theoretical analyses demonstrate that large edge dislocations, which are prohibited by the Frank energy criterion in 3D-materials, are stable in two-dimensional carbon nanotubes. Recent experimental high resolution transmission electronic microscopy(HRTEM) pictures also support our theoretical model, and show the existence of such large dislocations in nanotubes and their specific pseudo-climb.