We investigate NMR relaxation rates
1∕T1 of quantum spin chains in magnetic fields. Universal properties for the divergence behavior of
1∕T1 are obtained in the Tomonaga-Luttinger-liquid state. The results are discussed in comparison with experimental results.
The characteristics of the nuclear magnetic resonance (NMR), the contributions to the spin-lattice relaxation rate, and Knight shift of the resonance position are calculated exactly for a model spin-
1/2 XY chain with the magnetic impurity. It is shown that the deviations of the impurity's coupling to the chain and the effective impurity's
g factor from the values in the host spin chain yield special features in the temperature and magnetic field behavior for these NMR characteristics. The role of impurity-induced local levels in the NMR low-energy spin dynamics of spin chains is determined.