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Gallium nitride (GaN) and its allied binaries InN and AIN as well as their ternary compounds have gained an unprecedented attention due to their wide-ranging applications encompassing green, blue, violet, and ultraviolet (UV) emitters and detectors (in photon ranges inaccessible by other semiconductors) and high-power amplifiers. However, even the best of the three binaries, GaN, contains many structural and point defects caused to a large extent by lattice and stacking mismatch with substrates. These defects notably affect the electrical and optical properties of the host material and can seriously degrade the performance and reliability of devices made based on these nitride semiconductors. Even though GaN broke the long-standing paradigm that high density of dislocations precludes acceptable device performance, point defects have taken the center stage as they exacerbate efforts to increase the efficiency of emitters, increase laser operation lifetime, and lead to anomalies in electronic devices. The point defects include native isolated defects (vacancies, interstitial, and antisites), intentional or unintentional impurities, as well as complexes involving different combinations of the isolated defects. Further improvements in device performance and longevity hinge on an in-depth understanding of point defects and their reduction. In this review a comprehensive and critical analysis of point defects in GaN, particularly their manifestation in luminescence, is presented. In addition to a comprehensive analysis of native point defects, the signatures of intentionally and unintentionally introduced impurities are addressed. The review discusses in detail the characteristics and the origin of the major luminescence bands including the ultraviolet, blue, green, yellow, and red bands in undoped GaN. The effects of important group-II impurities, such as Zn and Mg on the photoluminescence of GaN, are treated in detail. Similarly, but to a lesser extent, the effects of other impurities, such as C, Si, H, O, Be, Mn, Cd, etc., on the luminescence properties of GaN are also reviewed. Further, atypical luminescence lines which are tentatively attributed to the surface and structural defects are discussed. The effect of surfaces and surface preparation, particularly wet and dry etching, exposure to UV light in vacuum or controlled gas ambient, annealing, and ion implantation on the characteristics of the defect-related emissions is described.