Twins are a pair of adjoining crystal grains related to each other by a special symmetry. They are frequently observed in bulk materials and nanomaterials. The formation of twins is an important topic in materials science and engineering because it affects material behaviors such as plastic deformation of metals, yield strength, and band gap energy in nanoscale semiconductors. Because of these unique phenomena and properties that the twinning can bring to the materials, it is of interest to investigate the formation of twins. Our primary objective in this dissertation is to study twinning in nanowires. Both gold and platinum <111> oriented nanowires were fabricated by similar solution-phase chemical synthesis methods. High-resolution transmission electron microscopy and electron diffraction patterns were carried out to analyze the structures of the nanowires. Nanodiffraction was used to demonstrate twinning is a general structural feature of the growth of gold nanowires growing in a <111> direction.  A model was proposed to explain the conditions under which twinning is energetically favored during nanowire growth. The model, which is based on a maximum rate hypothesis, considers the nanowire geometry and the relative surface and stacking fault energies and predicts twins should appear in gold nanowires but not in platinum nanowires, in agreement with experimental observations. During the structural characterization of gold nanowires, our interest is to resolve 3D structure of twinning. However, the structure of twinning in gold nanowires is very fine and the average spacing between twin boundaries is only 0.57nm (+/- 0.38 nm); therefore, regular 3D electron microscopy technique is unable to reconstruct these defected structures. Here we present a stereo vision technique to reconstruct 3D atomic non-periodic structures containing defects. The technique employs intrinsic atomic planes as epipolar planes to achieve the alignment accuracy needed to reconstruct a crystal with atomic resolution. We apply it to determine the 3D geometry and atomic arrangements of twinning in gold nanowire. In addition, an iterated cross-correlation algorithm was developed to analyze electron diffraction fully automatically to facilitate structural analysis of nanowires. A time-temperature-transformation diagram of platinum nanowires in chemical synthesis was determined to help optimize the fabrication process of the nanowires. / Ph. D.