Ion and dipole solvation kinetics is studied within the framework of the mean-spherical approximation (MSA). The solvation dynamics in nonassociated polar solvents involves a hierarchy of relaxation times in accordance with Onsager's "inverted snowball" picture. The average solvation time is determined by the relative solvent and solute sizes and by the dynamic screening. The dipole solvation is slower than ion solvation due to the shorter spatial range of interaction. The theoretical results are confronted with experimental data on time-resolved fluorescence shifts of dipolar probe molecules in nonassociated polar solvents. The experimental kinetic data exhibit a crossover from a short-time dipole solvation behavior to ion solvation at intermediate and long times. For associated polar solvents the Onsager picture has to be modified to account for structure breaking in the first solvation shell(s).