The numerical simulation of systems in which solids immersed in a fluid can come into contact is a challenging problem that raises significant modeling, mathematical, and numerical issues. It is of particular importance in biomedical applications, such as the simulation of cardiac valve dynamics, where accurate contact modeling is essential. Even in the absence of contact, fluid–structure interaction (FSI) problems are challenging due to moving geometries and potentially strong coupling between fluid and solid subsystems. When contact is included, additional difficulties arise: (i) in some configurations, FSI models with no-slip boundary conditions fail to predict contact; (ii) the straightforward introduction of contact constraints may lead to mechanically inconsistent fluid–structure–contact interaction models; and (iii) contact induces nonlinearly evolving interface conditions and disparate space and time scales. To address these issues, modified interface conditions and poroelastic roughness modeling of contacting solids have been proposed in the literature. In this talk, we consider several of these mechanically consistent modeling approaches and their unfitted CutFEM approximation. A comparison with alternative approaches is carried out within the framework of an international numerical benchmark.