The electronic structure, geometry, diffusion barriers and optical properties of fundamental defects of CsBr are calculated using hybrid functional DFT and TD-DFT methods. The B3LYP functional with a modified exchange contribution has been used in an embedded cluster scheme to model the structure and spectroscopic properties of the self-trapped triplet exciton, interstitial Br atoms and ions, self-trapped holes and Br vacancies. The calculated migration barriers and positions of maxima of optical absorption bands are in good agreement with experiment, justifying the obtained defect geometries. The off-center triplet exciton luminescence energy is also accurately calculated.