A wide range of applications requires an accurate description of the physical phenomena occurring in complex geometrical domains. The exploitation of subsurface resources or the geological disposal of wastes, the modeling of the behaviour of biological tissues or of biological processes, as few examples, asks for unconventional models targeted to accurate model liquids flow. Sometimes, the mathematical formulation of these problems requires a detailed description of immersed and intersecting objects, having one dimension which is order of magnitude smaller than other characteristic sizes of the physical domain, but crucial to obtain a reliable numerical solution. Chemical and mechanical interactions between the fluids and the surrounding structures also need to be carefully taken into account. This minisymposium is aimed at collecting the latest methods and models based on non-standard approximation strategies for effectively simulating complex phenomena on non-trivial domains.