This minisymposium focuses on recent advances in the mathematical modelling and numerical simulation of poromechanics, which describes the coupled interaction between deformable porous media and fluid flow. Such models are fundamental to applications in geomechanics, biomechanics, groundwater flow, geothermal energy, hydrogen storage, petroleum engineering, and carbon capture and storage. The session will highlight developments in robust and efficient high order numerical methods for solving the underlying multiphysics partial differential equations, including mixed finite element, discontinuous Galerkin, finite volume, virtual element, hybrid high-order, and structure-preserving discretizations. Particular emphasis will be placed on adaptive algorithms, multiscale methods, efficient iterative solvers, error estimation, uncertainty quantification, and emerging machine learning approaches. The aim of this minisymposium is to bring together researchers working on the mathematical analysis, numerical approximation, and scientific computing aspects of poromechanics. Particular emphasis will be placed on the design, analysis, and application of high-order discretizations for coupled porous media problems.