Constant-pressure constant-temperature MD simulations at ambient conditions have been carried out to evaluate three different potential models for DMSO, both as pure liquid and in the (1:3) DMSO-H2 O mixture, based on structural, thermodynamical, and dynamical properties. All the three models for DMSO: OPLS, P2, and NPS, the last one proposed by us, gave a good description of liquid DMSO. In combination with the SPC/E and TIP3P water models, these three potential functions were applied to predict excess mixing functions, reorientational correlation times and diffusion coefficients of the (1:3) DMSO-water binary system. Results obtained with the P2 and NPS models in combination with the SPC/E model for water agreed better with experiment than the OPLS model with either TIP3P or SPC/E water. The new NPS potential model was further used for an analysis of the spatial solvation structure around DMSO in the 1:3 mixture of DMSO-water, based on pairwise spatial distribution functions of atomic number densities. To reveal key structural features and molecular topologies beyond the first solvation shell, a new type of multiparticle spatial distribution function was introduced. Statistical analysis of the hydrogen-bond network, in the system with a large excess of acceptors, revealed DMSO·2H2O but not the previously suggested DMSO·3H2O complexes. Also the widely accepted picture of the DMSO·2H2O complexes needs a revision since many of these water molecules were further bound to nearby DMSO molecules. Moreover, another typical configuration, consisting of two DMSO and three water molecules, of which one was bridged to the two DMSO molecules, was found. In general, the heavy and slowly moving DMSO molecules are stronger competitors for available donated hydrogen bonds than water molecules.