We present here first principles hybrid functional calculations of the atomic and electronic structure of several iodine-related point defects in CsPbI3, a material relevant for photovoltaic applications. We show that the presence of neutral interstitial I atoms or electron holes leads to the formation of di-halide dumbbells of I-2(-) (analogous to the well-known situation in alkali halides). Their formation and one-electron energies in the band gap are determined. The formation energy of the Frenkel defect pair (I vacancies and neutral interstitial I atoms) is found to be approximate to 1 eV, and as such is smaller than the band gap. We conclude that both iodine dumbbells and iodine vacancies could be, in principle, easily produced by interband optical excitation.