Abstract: In this dissertation, we present several studies that employ density functional theory (DFT) to investigate physical principles underlying electron transport in nanostructures. Scanning tunneling microscopy and spectroscopy (STM/STS) experiments have been modeled using DFT calculations within the Tersoff-Hamann approximation, and the conductance and nonlinear I-V characteristics of several molecules have been studied using a method that combines the scattering-state formalism with DFT calculation techniques. We start with an introduction to density functional theory methods in Chapter One, followed by an application of these methods to study changes induced in boron nitride (BN) nanotubes under a transverse electric field in Chapter Two. Our calculations show that sufficiently strong fields can induce significant gap reduction and provide a way of tuning BN nanotube band gaps for applications. It was found that the band gap modulation increases with the nanotube diameter and is nearly independent of chirality. In Chapter Three, we performed DFT calculations to investigate recent scanning tunneling microscopy and spectroscopy (STM/STS) experiments performed on C₆₀ monomers adsorbed on Au(111) and Ag(100) substrates. Our calculations demonstrated that resonances in the STS spectra of C₆₀ on Au(III) and Ag(100) originate from C₆₀ HOMO, LUMO, and LUMO+1 states, and that the STM tip trajectory plays an important role in determining the spatial inhomogeneities of dI/dV images. Continuing the theme of combined STM/DFT studies in Chapter Four, we carried out an investigation of the elastic and inelastic tunneling properties of Gd@C₈₂ monomers adsorbed on Ag(100). Measurements show the dominant inelastic channel to be spatially localized in a particular region of the molecule, and calculations indicate that this channel arises from a vibrational cage mode. The observed inelastic tunneling localization is then explained as a consequence of strong localization of the electron-phonon coupling to this mode. To calculate transport properties across non-equilibrium aperiodic systems, we developed a method that combines DFT calculation techniques with the scattering-state formalism in Chapter Five. The semi-infinite nature of the leads is accounted for by using scattering-state wavefunctions to represent electron states and the chemical potential difference between the leads is reproduced by introducing shifts in the bulk-lead Hartree potential corresponding to the applied bias. This scattering-state method was then applied in Chapter Six to investigate a recent negative differential resistance (NDR) measurement, postulated to originate from current carried by a carbon atomic wire bridging carbon nanotube leads. Our calculations show that such junctions exhibit NDR and display clear even-odd behavior in the size of their currents, lending support to the postulate of carbon chain mediated NDR. In Chapter Seven, we applied our scattering-state method to study electron transport across a single hydrogen molecule sandwiched between Pd and Pt contacts. Substituting Pt contacts with Pd is found to result in a dramatic reduction in conductance, consistent with two recent break junction experiments. The computed drop in conductance is explained in terms of a qualitative change in transport behavior between the two systems. (Abstract shortened by UMI.)