Both the static and dynamic dielectric properties of water-dimethyl sulfoxide (DMSO) mixtures over the whole composition range are investigated by means of molecular dynamics (MD) simulations, and the results are compared with available experimental measurements. We discuss the behavior of the dielectric constant ana Kirkwood dipole correlation factor as functions of composition in terms of the self- and cross-species dipole density correlations and a suitable set of real space dipole-dipole distribution functions. We find that short-ranged structural correlations between neighboring water and DMSO molecules strongly influence the system＇s static dielectric properties, as expected on the basis of the molecular associations these mixtures are known to exhibit. In terms of the dynamics, we report time correlation functions for the mixtures＇ dipole densities and find that their long-time behavior can be reasonably well described by either biexponential or stretched exponential decays, which means that the dielectric relaxations of these mixtures are governed by complex,,multi time scale mechanisms of rotational diffusion. The dipole density relaxation time is a nonmonotonic function of composition passing through a maximum around 33% mole DMSO, in agreement with the experimental data for the mixtures＇ main dielectric relaxation time. Frequency-domain results such as the frequency spectra of the single-dipole time correlations and the experimentally accessible far-infrared absorption coefficient reveal that mixing also exerts a profound effect upon the librational dynamics of water molecules. This effect is much stronger than and qualitatively different from that observed in other associating aqueous mixtures and has been examined in view of new DMSO-water molecular aggregates suggested in previous MD works.