We present a theoretical study of the excitonic band edge states applied to the more commonly studied inorganic perovskite nanocrystals: CsPbBr3. We highlight the key role played by the electron-hole exchange interaction, including long-range and short range terms, in the positioning and splitting of dark and bright exciton sublevels, and discuss the influence of dielectric confinement, crystal field and shape anisotropy effects on the excitonic fine structure. The electron-hole exchange interaction splits the four excitonic states into three bright excitonic states at higher energy and a singlet dark state at lower energy. We find that, whatever the crystal phase, the bright-dark splitting is weakly sensitive to shape anisotropy. However, a strong enhancement, of about 50%, is obtained at the maximum of the dielectric contrast. For two crystalline symmetries, we particularly analyze how the bright exciton triplet energies vary, taking into account the states polarizations and considering the directions along which shape elongation/contraction applies. The main effect of the dielectric contrast is to increase significantly the exciton energies, for all the configurations. For a cubic crystal—Oh symmetry—the bright exciton triplet degeneracy can be partially or fully lifted with anisotropic shape along one or two directions, respectively. For a tetragonal crystal—D4h symmetry—the partial triplet degeneracy can be completely lifted by a single distortion from the cubic shape along a direction perpendicular to the tetragonal axis but a partial degeneracy is maintained for small distortions along the tetragonal axis. The amplitude of bright exciton splittings are basically driven by the shape anisotropy and is almost insensitive to the dielectric contrast. On the basis of this model, we discuss recent results on CsPbBr3 nanocrystals photoluminescence.