The dynamics of association of Na+-Cl-, Na+-Na+, and Cl--Cl- ion pairs in liquid dimethyl sulfoxide is studied by using the method of constrained molecular dynamics. Mean force potentials are employed to investigate the role of the solvent on the ion pairs. Friction kernels for the relative dynamics of the ion pairs have been evaluated at several interionic distances. Kramers and Grote-Hynes theories are applied to understand the passage of the ion pairs across the potential energy barrier existing between a contact ion pair and a solvent-separated ion pair. Transmission coefficients for the Na+-Cl- ion pair calculated from the above theories are in good agreement with the direct computer simulation results. The magnitudes of the squares of the nonadiabatic barrier frequencies are very large, and these confirm a polarization caging of the reactant ion pairs by the large solvent molecules.