In order to understand the chemical bonding of the binary indium bromides, we have performed both classical and quantum mechanical studies on all five crystallographically characterized phases (InBr, In5Br7, In2Br3, InBr2, and InBr3). Using a bond length-bond strength Ansatz, the different oxidation states-of indium can be satisfactorily described by taking 266.7, 242.0, and 240.3 pm as standard bond distances r(0) for In+-Br-, In2+-Br- and In3+- Br- interactions. On the basis of charge-self-consistent semiempirical bandstructure calculations, it is argued that the reduced phases (InBr, In2Br3, and In5Br7) are "soft" and easy to perturb upon chemical reaction (in the spirit of Pearson’s HSAB concept). Because of their electrophilicity, In2Br3 and In5Br7 may serve usefully as slightly acidic melts. Although coordination polyhedra around In+ ions are highly irregular because of the influence of the almost doubly filled indium 5s atomic orbital, the total In+-Br- bonding interaction is similarly weak in all cases, and the crystal potential around Inf seems to be very soft. In none of the cases, however, has there been found a directed electron "lone-pair" effect for In+. While In+-Br- bonds are characterized by antibonding contributions at the frontier bands (out-of-phase combination between indium 5s and bromine 4p orbitals), true In-in interactions can be found in the case of the In2Br62- species (In2+-In2+ single; bond) and in the structure of InBr, here playing a stabilizing role for the unusual 7-fold coordination geometry. Judging from energetic considerations, the probability of In+-In+ partial bonds as centric defects inside an otherwise acentric In2Br3 crystal structure is nonzero but small.