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Carbon nanotubes (CNT) constitute a new class of materials discovered in 1991 by Sumio Iijima that present unusual mechanical, electrical and thermal properties. Chemical Vapor Deposition (CVD) is the most promising synthesis route for producing large quantities of carbon nanotubes at a low cost. The first part of this thesis focuses on surface synthesis of high purity aligned carbon nanotubes using the CVD technique. High purity single wall and multi wall carbon nanotubes were grown using different substrates and catalysts. The substrates include non porous silicon substrates, porous silicon substrates, stainless steel substrates, stainless steel wires, and silicon cantilevers. The catalysts include molybdenum supported cobalt and alumina supported iron liquid catalysts, and iron and molybdenum catalysts deposited using e-beam evaporation and photolithographic techniques. Vertically aligned single wall and multi wall carbon nanotube forests were grown using the Easy Tube nanofurnace based on the CVD mechanism. The maximum length of the nanotubes grown was almost one millimeter and the diameters ranged from 1 to 100 nanometers. The nanotubes have a large surface area to volume ratio and a high electrochemical sensitivity. These properties may be useful for many applications such as reinforcing polymer composites, drug delivery, biomedical implants, neural imaging, development of biosensors for cancer detection, and other medical applications such as sensing and treating disorders like Epilepsy, Parkinson's disease, and Alzheimer's disease. Since nanotubes are proposed to be used for many biomedical applications, it becomes very important to understand the hazards of nanotubes and nanotechnology. Hence this thesis also presents a short overview of the toxicity of nanotubes. Carbon nanotube and nanofiber reinforced polymer composites have received tremendous amount of attention due to their interesting mechanical, electrical and thermal properties and potential applications. These composites potentially offer high stiffness, high strength, low electrical resistivity, dimensional stability, and light weight. Harnessing the unique physical properties of carbon nanostructures in materials applications has yet to be fully realized. The second part of this thesis mainly deals with improving the properties of composites using carbon nanofibers as fillers in an epoxy matrix. The single most important factor influencing use of carbon nanofibers as reinforcing fibers in polymer composites is their ability to effectively transfer the applied load in the matrix. The effective utilization of nanofibers in composites for structural applications depends strongly on the ability to disperse the nanofibers homogeneously in the matrix without damaging them. To be successfully used for enhancing the properties of composites, good interfacial bonding is required to achieve load transfer across the nanofiber-polymer interface. Hence, two main problems which arise in improving the properties are poor dispersion of the fibers in the composite and weak bonding between fibers and the matrix. These problems are attacked in this thesis by mechanical and chemical means. Solvent free functionalization, controlled sonication, high speed shear mixing at elevated temperatures, and high pressure casting are used to exfoliate the nanofibers in the epoxy. Pyrograf and CleanTech carbon nanofibers, which are similar to large diameter multi-wall carbon nanotubes, were used as filler materials in processing of composites. Incorporating 5 percentage by weight Pyrograf carbon nanofibers resulted in improvement of stiffness of the composite by about 45 percentage by weight and incorporating 5 percentage by weight CleanTech carbon nanofibers resulted in improvement of stiffness of the composite by 20 percentage by weight when compared to plain epoxy with out any nanofibers.