One-dimension (1D) nanostructures such as wires, rods, belts and tubes have become the focus of intensive researches for investigating structure-property relationships and related scientific and technological applications. Few-walled carbon nanotubes (FWNTs), a special type of small diameter multi-walled carbon nanotubes with superb structural perfection, are first discovered in our laboratory and systemically studied in this dissertation, including the synthesis by chemical vapor deposition (CVD) method, the purification and their applications. Moreover, iron phosphide nanorods/nanowires with controlled structures have been synthesized in solution phase and their magnetic properties have been investigated. The first parts of this dissertation are mainly focused on the studies of FWNTs synthesized by CVD method using binary catalyst Co (or Fe) with Mo (or W) supported on MgO made by modified combustion method. The structures of as-grown FWNTs can be controlled by three basic growth parameters: temperature, catalyst composition and carbon feeding rate. It is found that the as-grown FWNT materials prepared from W-containing catalysts are much more easily purified than those from Mo-containing catalysts. Both raw and purified FWNTs show enhanced electron field emission characteristics compared to other current commercial nanotubes. The highly pure FWNTs are then used to prepare composite materials with polymers and noble metal nanocrystals. Furthermore, the structures of FWNTs are attempted to be controlled by adjusting the growth parameters of carbon monoxide CVD. Highly pure DWNTs (over 95%) are obtained and well characterized by TEM, Raman and fluorescence spectrum. The optical properties of DWNTs and their application in bio-imaging are primarily investigated. In addition, conducing films are fabricated using highly pure FWNTs and the relationship between the structure and the conductivity is surveyed and further possible improvements are discussed. The second parts of this dissertation describe a solution-phase route for the preparation of single-crystalline iron phosphide nanorods and nanowires. The mixture of trioctylphosphine oxide (TOPO) and trioctylphosphine (TOP) which are commonly used as the solvents for semiconductor nanocrystal synthesis is not entirely inert. TOP serves as phosphor source and reacts with Fe precursors to generate iron phosphide nanostructures with large aspect ratios. In addition, the morphology of the produced iron phosphide structures can be controlled by the ratio of TOPO/TOP. A possible growth mechanism is discussed. / Dissertation