NMR line shapes for polycrystalline samples under static, sample spinning and molecular dynamic exchange motion have been investigated. Of particular interests are the line shapes of quadrupole nuclei under the above conditions. The line shapes governed by the following conditions are discussed. (1) The field dependence of the NMR static powder line shape in the presence of both shift anisotropy and the second order quadrupole interaction of half integer quadrupolar nuclear spins are studied. From the field dependence of the critical frequencies, the interaction parameters as well as the mutual orientation of the interaction tensors can be conveniently determined. This method, never before proposed, provides an easy approach in determining the locations and the local electronic environments of the quadrupole nucleus. (2) The powder spectrum of the second order quadrupole interactions in the presence of rapid sample spinning has been studied for ('133)Cs (I = 3/2) nucleus in the Zeolite. The changes of the quadrupole coupling constants and the asymmetry parameters provides a reasonable indication of the process of the hydration of the sample. (3) The dynamic NMR powder spectra of the second order quadrupole interaction plus nonnegligible shift anisotropy has been studied in detail for the ('23)Na (I = 3/2) nucleus in the compound NaMo(,4)O(,6). This study provides information concerning the equilibrium location of the sodium nucleus and indicates a structural incommensuration. The effect of molecular dynamics upon the second order central transition has been demonstrated for the first time. (4) The variable-angle sample spinning line shape of a spin-half nucleus under a heteronuclear dipolar interaction between the quadrupole spin and the spin-half nucleus is strongly dependent upon the quadrupole moment and the asymmetry of the quadrupole nucleus. Hence it provides an indirect tool in studying the quadrupole nucleus in a manner not possible to probe by conventional NMR. These studies have been applied to distinguish the different structural sites in Zr(,6)Cl(,12)H and ZrClO(,x)H(,y) which are produced in mixed form during synthesis.