This minisymposium aims to bring together leading researchers working on the analysis and application of hybrid and polytopal discretization methods. Particular emphasis will be placed on the development of novel numerical schemes for coupled partial differential equations (PDEs) arising in complex multiphysics problems, including interface-coupled systems and heterogeneous media. The session will cover recent advances in the design, analysis, and implementation of discretization techniques for problems in continumm mechanics. Contributions addressing spectral approximations and eigenvalue problems associated with these formulations are also strongly encouraged.