Nuclear magnetic relaxation helps in unfolding the pattern of molecular motion in polymer solutions. Information on both solvent and polymer motions can be obtained by appropriate experiments. Examples are given using T1 and T2 measurements on polyethylene oxide, polydimethylsiloxane, polyisobutylene and other systems. Several general features appear in nuclear relaxation of the polymer molecules. T1 is insensitive to the molecular weight of the polymer and to the concentration of the solution up to about 20 % concentration. T1 depends on solvent viscosity though the variation appears to be less pronounced than that predicted by Bloembergen-Purcell-Pound theory. T2, on the other hand, is a function of polymer concentration, and drops rapidly with concentration at high molecular weights. This is in accord with what is known about entanglements in polymer solutions. T1 and T2 are not changed by replacing hydrogen-containing solvents with deuterated substitutes. The rate of solvent motion is too rapid to be effective in nuclear relaxation of the polymer. T1 and T2 measurements on the solvent in polymer solutions can be analyzed in detail by selective replacement of hydrogen by deuterium. This has been done in the poly(methylmethacrylate)+ benzene system. An apparent anomaly of solvent T2 in solutions of high molecular weight polymer is explained in terms of a fluctuating chemical shift.