Luminescence of excitons bound to five point defects and one complex neutral acceptor has been identified in GaP. These excitons are weakly bound, and have weak no-phonon lines because of the symmetry of the electron in the exciton. The high degeneracy of this electron in GaP, resulting from the multivalleyed conduction band, together with the allowed states for the combination of two $j=\frac{3}{2}$ holes, gives 12 possible distinct no-phonon lines in the exciton transition, many of which have been seen for the shallower acceptors. These bound excitons obey a modified form of Haynes's rule. This fact, the magnitude of the exciton localization energies and the magneto-optical properties of these excitons firmly establish the nature of these transitions. Mirror symmetry is exhibited between the absorption and luminescence spectra of the Zn exciton, and the time for radiative decay has been determined. This is 500 times longer than the measured luminescence decay time, because of the predominance of the Auger recombination channel. The radiative decay times of these shallow excitons are nearly independent of the acceptor. The dependence of the Auger life-times ${\ensuremath{\tau}}_{E}$ on the binding energies of the exciton complexes have been established for the first time. It is shown that ${\ensuremath{\tau}}_{E}\ensuremath{\propto}{E}_{A}^{n}$, where $n\ensuremath{\sim}\ensuremath{-}4.5$, close to the value (-4.0) predicted from a hydrogenic model with a single spherical valence band. It is clear that deeper (neutral) acceptors form highly nonradiative recombination centers for excitons, with very short decay times. Strong complex satellites in the acceptor-exciton luminescence may involve phonons associated with the dynamic Jahn-Teller effect. Weaker "two-hole" luminescence transitions have been tentatively identified for the Zn and Cd acceptors. If this identification is correct, different types of final hole states are seen for these two acceptors.