Abstract Infiltration regulates the movement and storage of water at the soil–atmosphere interface and is, therefore, a key component of many related physical and biogeochemical processes. Numerous studies have examined infiltration over the past two centuries. These efforts have resulted in the development of numerous models that capture the effects of specific soil properties and initial and boundary conditions. This proliferation of models has advanced our collective ability to understand infiltration processes but has also made it challenging for researchers to select appropriate approaches for analyzing experimental infiltration data or for conducting basic research on soil parameters like saturated hydraulic conductivity or sorptivity. Here, we aimed to reduce this uncertainty by developing a comprehensive literature review of published infiltration models, including their underlying philosophies and evolution over the years. Through this effort, we compiled and examined 138 unique infiltration models. We grouped models into two major categories, empirical and conceptual, noting that boundaries between those two categories are at times debatable. After classifying and providing a full historical retrospective of these models, we examined specific model parameters and how their usage has changed with time. We also reviewed different methods applied to estimate infiltration parameters, as well as the challenges that arise when using such methods. Finally, we proposed a framework for identifying suitable models depending on field conditions, experimental plan, and data availability.