Excitons in Bridgman grown halide perovskite CsPbBr3 single crystals were examined using photoluminescence (PL) spectroscopy to determine the nature of the electronic states. The photoluminescence intensity was strongly temperature-dependent and depended upon the specific exciton band. At low temperatures intrinsic disorder and its related shallow below bandgap tail states determine the emission properties. Photoluminescence at low temperature revealed the presence of several strong bands at the band edge that is attributed to free or trapped/bound excitons. This PL emission results from strong electron-phonon coupling with an average phonon energy Eph of 6.5 and 27.4 meV for the emissions, comparable to that observed in other perovskites. The Huang-Rhys parameter S was calculated to be 3.81 and 1.51, indicating strong electron-phonon coupling. The interactions between electrons and phonons produce small polarons that tend to bind charge carriers and result in trapped/bound excitons. The transient photoluminescence response of each specific band was studied, and the results indicated a multiphonon recombination process. Average PL lifetimes of ∼17 ns for free excitons and ∼38 ns for trapped/bound excitons were determined. The observed edge states could be associated with native defects such as vacancies and interstitials, as well as twinning due to the cubic-to-tetragonal phase transition in CsPbBr3. Elimination of the trapping sites for binding excitons could lead to improved charge transport mobilities, carrier lifetimes, and detector properties in this system.