Facing global warming’s consequences is a major issue in the present times. Regarding the climate, projections say that heavy rainfalls are going to increase with high probability together with temperature rise; thus, the hazard related to rainfall-induced shallow landslides will likely increase in density over susceptible territories. Different modeling approaches exist, and many of them are forced to make simplifications in order to reproduce landslide occurrences over space and time. Process-based models can help in quantifying the consequences of heavy rainfall in terms of slope instability at a territory scale. In this study, a narrative review of physically based deterministic distributed models (PBDDMs) is presented. Models were selected based on the adoption of the infinite slope scheme (ISS), the use of a deterministic approach (i.e., input and output are treated as absolute values), and the inclusion of new approaches in modeling slope stability through the ISS. The models are presented in chronological order with the aim of drawing a timeline of the evolution of PBDDMs and providing researchers and practitioners with basic knowledge of what scholars have proposed so far. The results indicate that including vegetation’s effects on slope stability has raised in importance over time but that there is still a need to find an efficient way to include them. In recent years, the literature production seems to be more focused on probabilistic approaches.
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