Preparation and characterization of inorganic materials is a crucial practice because understanding the relationship between structure and property is important for improving current performance and developing novel materials. Many metal centers in technologically and industrially important materials are unreceptive low- quadrupolar nuclei (i.e., possessing low natural abundance, low NMR frequencies and large quadrupole moments) and they usually give rise to very broad NMR resonances and low signal-to-noise ratios, making it difficult to acquire their solid-state NMR spectra. This thesis focuses on the characterization of inorganic materials using solid-state NMR (SSNMR) spectroscopy at very high magnetic field of 21.1 T in combination with quantum chemical calculations for computational modeling. In the first part of this thesis, 67Zn and 17O SSNMR studies of several microporous materials were reported. The results of 67Zn SSNMR studies from several important metal-organic frameworks (MOFs), in particular, zeolitic imidazolate frameworks (ZIFs) were presented. 67Zn SSNMR spectroscopy was used to gain structural information regarding the desolvation process in MOF-5. Furthermore, 67Zn SSNMR spectroscopy were utilized to study the host-guest interactions in ZIF-8 loaded with different guest molecules. Static 67Zn SSNMR spectra of microporous zinc phosphites (ZnP) and zinc phosphates (ZnPO) were also acquired at natural abundance. The Gaussian calculation results on a model cluster for ZnP indicate that Zn-O bond length is the most dominant factor to the observed quadrupolar coupling constant (CQ) among other geometric parameters around Zn centres. The local structures of the framework oxygen sites in molecular sieve SAPO-34 were directly probed by several 17O SSNMR techniques. The involvement of water vapor during the SAPO-34 formation in dry-gel conversion (DGC) synthesis was also investigated. In the second part, 91Zr and 33S SSNMR spectra of layered zirconium phosphates (ZrP) and transition metal disulfides (MS2) were obtained. The empirical correlations between NMR parameters and various structural parameters were used for obtaining partial structural information in Li+ and Co(NH3)63+ exchanged layered ZrP. For a series of closely related MS2 materials, the observed differences in the CQ(33S) values were rationalized by considering the difference in their geometrical arrangements. The final part of this thesis featured two examples of SSNMR spectroscopy of exotic nuclei in some interesting inorganic materials. (i) The experimental 135/137Ba SSNMR spectroscopy and theoretical studies of -BBO, an important non-linear optical (NLO) material, indicate that the true crystal structure of -BBO is R3c space group rather than R3. (ii) An ultrahigh field natural abundance 73Ge SSNMR study of two representative germanium containing materials [GeCl2-dioxane and GePh4] demonstrated that acquiring 73Ge wideline NMR spectra of germanium compounds where the Ge experiences an extremely large quadrupolar interaction is feasible and that the small 73Ge chemical shielding anisotropy (CSA) can be directly measured.