CsCdBr3 adopts the pseudo-one-dimensional CsNiCl3 structure. It consists of chains of face-sharing [CdBr6](4-) -octahedra separated by parallel chains of Cs+ ions. Numerical calculations show that it possesses a narrow isolated conduction band of Cd s-electrons, The well-known symmetry of this band allows the analysis of its optical transitions from and to the different branches of the valence band by symmetry selection rules. The symmetries of the branches can be determined by means of the corresponding LCAO molecular orbitals. The analysis of the optical and near UV spectra shows that the "optical" band gap exceeds significantly that of energy. Thus there is a number of optically inactive or "silent" electronic states within the optical band gap. These states are responsible for a number of surprising effects at dopant rare-earth ions as e.g. fast nonradiative transitions, fast quantum upconversion, and resonantly enhanced crystal-field splittings.