The inter- and intra-molecular dynamics of aqueous dimethyl sulfoxide (DMSO) solutions have been measured using optical heterodyne-detected Raman-induced Kerr effect spectroscopy. Solutions were studied over the entire range of composition at 294 K. The Kerr transients characterize both the underdamped inter- and intra-molecular vibrational motions, as well as the overdamped, diffusive orientational motions. The longer diffusive relaxation time constant tau(2) is assigned to DMSO reorientation, and varies strongly with mole fraction of DMSO. The shorter time constant tau(1) is assigned to water reorientation, and the value of 1.0 ps is nearly invariant across the range of solution composition. The solutions deviate substantially from hydrodynamic scaling behavior, since the ratio of DMSO reorientation time constant normalized by shear viscosity tau(2)/eta is not a linear function of mole fraction. The peak frequencies for three of five low frequency intramolecular vibrations decrease with increasing water content. Both anisotropic and isotropic Kerr transients are recorded. The isotropic Kerr transient is dominated by the partially depolarized nu(10) symmetric C-S-C stretching vibration at 670 cm(-1). Electronic structure calculations for isolated DMSO, perdeuterated DMSO (d(6)-DMSO), and water are carried out using semi-empirical (PM3), density functional (B3LYP), and MP2 methods. Basis sets up to 6-311++G(d,p) are used and vibrational frequencies are calculated within the harmonic approximation. An unusual hemispherical shape is obtained for the electrostatic potential (ESP) about the DMSO oxygen. This hemispherical ESP was consistently observed for all levels of electronic structure theory and all basis sets that were used. Calculated polarizabilities permit us to estimate the anisotropic Kerr signal for an isolated DMSO molecule to be 79 times greater than for an isolated water molecule.