The numerical simulation of poromechanics, the behavior of fluid-saturated porous media, has become of importance in several branches of natural sciences and technology for analyzing experimental data or designing theories and therapies based on mathematical concepts. In the case of fluid injection in porous media it is important for the assessment of the fluid storage capacity of the medium to accurately model and simulate the mechanical response, i.e., the deformation, of the porous media. Poroelastic waves, partial saturation, the incorporation of two- or multiphase flow, thermal processes and/or large deformations in general lead to nonlinear and even more complex mathematical models that require physically correct (structure-preserving) discretization and robust iterative solution methods. The range of physical parameters puts an additional facet of complexity on the of numerical methods. Recently, a particular focus has been put on monolithic solvers as well as iterative coupling schemes for the coupled subsystems of fluid flow and mechanical deformation. In practice, input data often entail uncertainty and methods for its quantification are of great importance, too. There is also a need to design and analyze new models or further development in porous media with fractures, multi-compartmental, nonlinear or fully dynamic systems. Contrary to linear models, the accurate numerical solution of nonlinear poromechanics problems in general is more involved and its reliability much more difficult to guarantee. This can be due to nonlinearities of various kinds, e.g., in constitutive relations, boundary conditions, functionals in variational formulations of error control or optimization problems. Important questions to be addressed in this context concern the stability and convergence of approximations, adaptive numerical methods, a priori and a posteriori error estimates as well as robust iterative solution methods. The mini-symposium provides a forum for the presentation and discussion of progress in the above-mentioned fields.