The work in this dissertation presents studies of three distinct areas of interest in the field of quasicrystals: bulk structure, transport properties, and electronic structure. First, we describe the results of a study which explored the fundamental interactions between the atomic species of the icosahedral Al-Pd-Mn quasicrystal. This study was done using laser vaporization to create gas-phase metal clusters, which were then ionized and analyzed using time-of-flight mass spectrometry. Both the kinetic and thermodynamic stabilities of the clusters were probed.;Second, we report our investigations of the bulk thermal transport properties of a decagonal Al-Ni-Co quasicrystal in the temperature range 373K--873K. The properties of a sample oriented along the periodic, aperiodic, and 45° axes were measured. A high degree of anisotropy was observed between the aperiodic and periodic directions. The results of the 45° off-axis data were compared with theoretically predicted values. Transport behavior is described in terms of charge carriers and the mean-free time between carrier collisions. It is concluded that the mean-free time is much longer in the periodic direction than in the aperiodic direction, producing the observed anisotropy in thermal transport.;The third study presents a detailed analysis of the sputter-induced phase transformation which occurs on the 5-fold surface of an icosahedral Al-Cu-Fe quasicrystal. Reflection high-energy electron diffraction, x-ray photoemission spectroscopy, and ultra-violet photoemission spectroscopy data were collected as a function of annealing temperature and were used to probe surface structure, surface composition, and electronic structure, respectively. The composition and structure of the sputtered surface are consistent with a transformation to the beta-Al-Cu-Fe cubic structure, and shows a sharp metallic cut-off in the spectral intensity of the electronic structure at the Fermi edge. Upon annealing the surface reverts to a quasicrystalline composition and structure. This is correlated with a reduction in spectral intensity at the Fermi level. It is concluded that this is due to the opening of a pseudo-gap in the electronic density of states as the surface reverts from beta-Al-Cu-Fe to quasicrystalline.