The photoluminescence (PL) decay of hybrid halide perovskite single crystals (MAPbX(3), MA = CH3NH3+, Pb = Pb2+, X = Br-, and I-) is measured over 4 orders of magnitude in intensity over the time scales of 100s of nanoseconds to a few microseconds. This long PL decay is non-exponential, suggesting the presence of a distribution of carrier relaxation times. Spectro-temporal studies show that the emission peak red-shifts with increasing time. The physics of this problem is closely related to donor-acceptor pair recombination in crystalline semiconductors and recombination in a-Si:H. Based on these models, we present a simple model to account for the recombination dynamics in the perovskite systems. This model also accounts for the fluence dependence of the recombination kinetics. In this model, a fraction of the photogenerated electrons and holes are trapped in localized states. The electrons tunnel to the hole sites for recombination. The broad distribution of lifetimes is a consequence of the fact that the tunneling probability is very sensitive to the separation of electron-hole pairs, and PL decay dynamics is a function of excitation fluence, i.e., carrier density generated by optical excitation. The red-shift arises from the fact that holes and electrons are trapped at different energies.