Microcrystalline powders of Bi3+-doped Lu3Ga5O12 garnet are investigated by the X-ray diffraction, time-resolved luminescence spectroscopy, and thermally stimulated luminescence methods. The mechanisms of the processes are clarified, which take place in the excited states of the Bi3+-related luminescence centers and result in the appearance of two (ultraviolet and visible) emission bands with strongly different characteristics in the photo- and thermoluminescence spectra as well as in the creation of stable electron and hole centers of different types. The conclusion is made that besides the electron transitions between the Bi3+ levels, the photoexcitation of Lu3Ga5O12:Bi results in the ionization of Bi3+ and in the Bi3+ → Ga3+oct, Bi3+ → Ga3+tetr, and Bi3+ → Lu3+ electron transfer transitions. These processes can lead to the release of free electrons into the conduction band, their trap at different electron traps, and formation of hole centers of the type of Bi4+ and {O- - Bi3+}. The recombination of electrons with these hole centers results in the ultraviolet emission of a Bi3+ ion and visible emission of an exciton localized around the Bi3+ ion, respectively.