Bi-doped compounds recently became the subject of an extensive research due to their possible applications as scintillator and phosphor materials. The oxides co-doped with Bi³⁺ and trivalent rare-earth ions were proposed as prospective phosphors for white light-emitting diodes and quantum cutting down-converting materials applicable for enhancement of silicon solar cells. Luminescence characteristics of different Bi³⁺-doped materials were found to be strongly different and ascribed to electronic transitions from the excited levels of a Bi³⁺ ion to its ground state, charge-transfer transitions, Bi³⁺ dimers or clusters, radiative decay of Bi³⁺-related localized or trapped excitons, etc. In this review, we compare the characteristics of the Bi³⁺-related luminescence in various compounds; discuss the possible origin of the corresponding luminescence centers as well as the processes resulting in their luminescence; consider the phenomenological models proposed to describe the excited-state dynamics of the Bi³⁺-related centers and determine the structure and parameters of their relaxed excited states; address an influence of different interactions (e.g., spin-orbit, electron-phonon, hyperfine) as well as the Bi³⁺ ion charge and volume compensating defects on the luminescence characteristics. The Bi-related luminescence arising from lower charge states (namely, Bi²⁺, Bi⁺, Bi⁰) is also reviewed.