Among the important family of halide perovskites, one particular case of all-inorganic, 0-D CsPbBr and 3-D CsPbBr-based nanostructures and thin films is witnessing intense activity due to ultrafast luminescence with high quantum yield. To understand their emissive behavior, we use hybrid density functional calculations to first compare the ground-state electronic structure of the two prospective compounds. The dispersive band edges of CsPbBr do not support self-trapped carriers, which agrees with reports of weak exciton binding energy and high photocurrent. The larger gap 0-D material CsPbBr, however, reveals polaronic and excitonic features. We show that those lattice-coupled carriers are likely responsible for observed ultraviolet emission around ∼375 nm, reported in bulk CsPbBr and CsPbBr/CsPbBr composites. Ionization potential calculations and estimates of type-I band alignment support the notion of quantum confinement leading to fast, green emission from CsPbBr nanostructures embedded in CsPbBr.