Bromine-79/81 solid-state NMR (SSNMR) spectroscopy is established as a tool to characterize the local structure and symmetry about bromide ions in inorganic systems. Benchmark experimental 79/81Br SSNMR data are acquired for CaBr2, SrBr2, BaBr2, MgBr2·6H2O, SrBr2·6H2O, BaBr2·2H2O, and CaBr2·xH2O using the Solomon echo and/or QCPMG pulse sequences in magnetic fields of 11.75 and 21.1 T. Analytical line-shape analysis provides 79/81Br electric field gradient (EFG) tensor parameters (including 79Br quadrupolar coupling constants, C
Q(79Br), of up to 75.1(5) MHz in CaBr2), chemical shift tensor parameters (including the largest reported anisotropy), and the relative orientation of the tensor principal axis systems. These data are interpreted in terms of structure and symmetry. Our results indicate that ionic bromide systems should be generally accessible to characterization by 79/81Br SSNMR despite sizable quadrupolar interactions. The resolving capabilities of 79/81Br SSNMR spectroscopy are illustrated, using samples which possess up to four magnetically inequivalent sites, and through a rare example of 79Br magic-angle spinning NMR for a Br in a noncubic lattice. Bromine-79/81 SSNMR spectroscopy is demonstrated to be sensitive to the presence of hydrates (i.e., pseudopolymorphism), via drastic changes in C
Q and δiso. The changes are diagnostic to an extent that the composition of the mixture CaBr2·xH2O is determined for the first time. This technique should therefore be applicable to characterize other unknown mixtures or polymorphs. Important instances where 79Br nuclear quadrupole resonance data were found to be deficient are noted and corrected. GIPAW DFT computations are shown to be generally in very good agreement with the experimental 79/81Br SSNMR observations. Finally, it is demonstrated that the origin of the EFG at the Br nuclei cannot be described quantitatively using a point charge model, even after including Sternheimer antishielding effects.