The coupled-cluster method with a large basis set with quasi-relativistic effective core potentials on the halogens was utilized to investigate the ground electronic state X(1)Sigma (+) of the IHBr anion. A semi-global, three-dimensional potential energy surface was obtained via spline interpolation of ab initio data. Variational rovibrational calculations were carried out with this potential energy surface, and assignment of fundamentals and low-lying overtones, as well as combination bands, is presented for IH(D)Br anions. Photodetachment spectra for IH(D)Br- + hv-->[IH(D)Br] + e(-) were computed using three-dimensional time-independent real and complex L-2 methods and a recently developed real L-2 wave packet propagation technique; all methods employed a previous London-Eyring-Polanyi-Sato empirical potential for the neutral system. Well resolved fine structure is found in photodetachment spectra of IHBr-. This structure is assigned to bending excitation based on analysis of the wave functions and the neutral potential energy surface near the Franck-Condon region. This fine structure is largely eliminated in the IDBr- spectrum. The photodetachment spectrum for the first excited asymmetric stretch of IHBr- shows a new feature that is associated with sampling of the transition state region of the neutral surface. Spin-orbit corrected multi-reference configuration interaction calculations indicate that the first excited electronic state is only about 0.06 eV above the ground electronic state of the neutral IHBr system in the Franck-Condon region. The model empirical potential used in the calculations of photodetachment spectra is shown to have roughly the average behavior of these two ab initio potentials.