The kinetics of vapor phase hydration (VHT) of high-sodium waste glasses often exhibits incubation, fast-rising, and final stages. The incubation stage is characterized by the slow and gradual appearance of transformed regions on the surface of the glass, signaling the initiation of the phase transformation. This is followed by a fast-rising stage, during which most of the transformation takes place. The final stage is characterized by the slower alteration of the remaining glass phase, which can have a duration orders of magnitude longer than those of the previous stages. While the Avrami equation provides a good representation of these features, the origin of the late-stage slow-down in the Avrami model is unrealistic for the VHT process. Computer simulations based on cell models have been used to investigate possible mechanistic origins. The models consider the formation of multiple alteration phases and simulate the complex interplay among the several microscopic mechanisms involved in the hydration process. The models assume that the transformation from the original pristine glass to the final stable altered phase occurs in two steps: from glass to a metastable phase, and then from a metastable to a stable phase. The results indicate that the late-stage slow-down can be reproduced as a result of the build-up of species that are incompatible with the stable phase or by the occlusion of the surface due to the growth of a surface phase that is less permeable to water. The simulation results are in good general agreement with the features of the experimental data.