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 Br-79/81 SSNMR data are acquired for CaBr2, SrBr2, BaBr2, MgBr2 center dot 6H(2)O, SrBr2 center dot 2H(2)O, BaBr2 center dot 2H(2)O, and CaBr2 center dot xH(2)O using the Solomon echo and/or QCPMG pulse sequences in magnetic fields of 11.75 and 21.1 T. Analytical line-shape analysis provides Br-79/81 electric field gradient (EFG) tensor parameters (including Br-79 quadrupolar coupling constants, C-Q(Br-79), 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 Br-79/81 SSNMR despite sizable quadrupolar interactions. The resolving capabilities of Br-79/81 SSNMR spectroscopy are illustrated, using samples which Possess LIP to four magnetically inequivalent sites, and through a rare example of Br-79 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 delta(iso). The changes are diagnostic to ail extent that the composition of the mixture CaBr2 center dot xH(2)O is determined for the first time. This technique should therefore be applicable to characterize other unknown mixtures or polymorphs. Important instances where Br-79 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 Br-79/81 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.