Based on a model of coupled processes with differently time-dependent decay kinetics we present a critical review on photoluminescence (PL) and transient absorption (TA) experiments in undoped and Mg or Fe-doped LiNbO3, together with a comprehensive interpretation of visible radiative and parallel non-radiative decay processes on timescales ranging from 50 ns up to minutes. Analogies and peculiarities of the kinetics of mobile self-trapped and pinned excitons are investigated and compared with those of hopping polarons in the same system. Exciton hopping with an activation energy of ≈0.18 eV is shown to govern the lifetime and quenching of the short PL component above 100 K. Strong interaction between excitons and dipolar pinning defects explains the exorbitant lifetimes and large depinning energies characterizing delayed TA components in doped LiNbO3, while restricted hopping of the pinned excitons is proposed to play a role in strongly delayed PL in LiNbO3:Mg exhibiting a narrowed emission band due to locally reduced electron-phonon coupling. Atomistic models of pinned excitons are proposed corresponding to charge-compensated dipolar defects predicted by theories of dopant incorporation in LiNbO3 and are systematically assigned to absorption bands observed near the UV edge. Excitation in these bands is shown to lead directly to pinned exciton states confirming also the previously proposed two-step exciton-decay scenario in LiNbO3:Fe. Weak intrinsic sub-80 ns luminescence in congruent LiNbO3 is explained as an opposite effect of enhanced electron-phonon coupling for excitons pinned on NbLi antisite defects. The comparison of the different observed stretching behaviors in the paradigmatic system LiNbO3 provides an intuitive picture of the underlying physical processes. The findings are relevant not only for holographic and non-linear optical applications of LiNbO3 but are of general interest also for the treatment of stretched exponential or other time-dependent kinetics in complex condensed systems ranging from nanocrystals and polymers to liquids and biophysical systems.