CsCdBr3 has a quasi-linear crystal structure. It consists of covalently bound [CdBr](6)(4-) chains separated by chains of Cs+ ions. The trivalent rare-earth (RE) ions substitute for divalent Cd ions forming predominantly pair centers of the type RE3+-(Cd vacancy)-RE3+. A minority of RE ions forms "single-ion" centers with more distant charge compensation. The electronic structure around the band gap is determined by the [CdBr](6)(4-) octahedra. The lowest excitonic states of the lattice are charge-transfer states of these octahedra. At low temperatures they form self-trapped excitons which become mobile around 80 K.