This talk examines the behavior of liquids spreading on soft polymeric substrates. When a thin layer of liquid flows over a soft material, its movement is primarily driven by surface tension, while effects like inertia and gravity are typically negligible. The soft substrate can deform, which means that the liquid and the surface interact in more complex ways. The presentation discusses how to model these interactions in a way that is consistent with thermodynamic principles with sharp or diffuse interface, including extensions to account for diffusion in the material. In addition, the talk covers numerical discretization techniques that enable computer simulations to accurately represent these processes. Overall, the presentation addresses key mathematical challenges and offers new perspectives on the dynamics of wetting on soft substrates.