Facing global warming consequences is a major issue of present times. For what concerns climate, projections say that heavy rainfalls are going to increase with high probability together with temperature rise, thus also the hazard related to rainfall induced shallow landslides will likely increase in density over susceptible territories. Different modeling approaches exist and any of them is 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 on the different involved processes. In this paper, a narrative review about 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), the inclusion of new approaches in modeling slope stability through the ISS. Models are presented in chronological order with the aim of drawing a timeline of the evolution of PBDDMs and to give researchers and practitioners a basic knowledge on how much has been already done. Results indicate that including vegetation effects on slope stability has raised in importance over time but that there is still the need of finding an efficient way to include them, and that in the last years the literature production seems to be more focused on probabilistic approaches.