Graphene and carbon nanotubes have drawn much attention in the last decade, and functionalization of these materials is considered a great technique for manipulating them. In this project, we mainly investigated functionalized double-wall carbon nanotube and functionalized graphite. Due to the unique physical structure of double-wall carbon nanotubes (DWNTs), the outer tube can be chemically functionalized while the inner tube is left in pristine condition. The diameter of bare DWNTs is around 2-3 nm as measured by scanning tunneling microscopy (STM), but fluorinated DWNTs possess much larger diameters, from 3-10 nm, due to a stronger electronic interaction. In addition to imaging the as prepared material, the material was imaged after annealing at temperatures up to 1000 K. Due to the defluorination, the diameter is decreased to that of the initial bare DWNTs and atomic resolution of the lattice was recovered. In addition, it was possible to observe the initial and final structures on the same nanotubes and the evolution of their associated defect structures. Lastly, Raman spectroscopy was employed to confirm the defluorination by revealing the recovery of the radial breathing mode which disappeared upon fluorination. Also, we investigate the epoxidation mechanism on graphite surfaces with STM and Raman spectroscopy, and our results indicate that the functionalzation occurs on the edges, not on the basal plane as reported previously.