Single wall carbon nanotubes (SWNTs) are novel materials with unique chemical and physical properties: they are the strongest fiber ever made; they have outstanding thermal conductivity and unique one dimensional electrical conductivity; their weight is light and their individual size is only 0.4 to several nm in diameter. A wide range of applications of SWNTs were proposed including high performance polymer composites, field emitter for flat panel display, energy storage, molecular electronics and biomedical applications, etc. Functionalization of SWNTs has been an important pathway to utilize SWNTs for many of these applications. This thesis studies the fluorination of SWNTs, electrochemical properties of fluorinated SWNTs as a cathode material in lithium batteries and oxidative properties and thermal stabilities of fluorinated SWNTs in a binary metal compound matrix. This thesis also studies functionalization of SWNTs through a free radical addition process, in which radicals were from the thermal decomposition of organic diacyl peroxides including lauryl peroxide, benzoyl peroxide, succinic acid peroxide and glutaric peroxide. Functionalized SWNTs prepared from this method have improved solubility in various common organic solvents. They are characterized with a variety of techniques including Raman, FTIR, TGA/MS, TEM and solid state 13C NMR. A parallel study on C60 fullerene is also included. The succinic acid peroxide is of particular interest for functionalization because it can attach ethylenecarboxyl groups (--CH2CH 2COOH) to the sidewall of SWNTs. The sidewall acid groups, after reacting with thionyl chloride and diamines, are converted to terminal amine groups, which can form covalent bonds with epoxy polymers to prepare SWNT reinforced epoxy polymer composites. Mechanical tests show that the tensile strength, elongation and storage modulus of epoxy are greatly improved (25∼30%) with 1 weight percent of SWNTs addition.