Porous materials are characterized by complex interactions between the deformation of a solid skeleton and the resulting flow of an interstitial fluid. Themodynamically consistent models such as the Theory of Porous Media (TPM) result in a set of coupled, non-linear partial differential equations (PDE). To reduce computational complexity, linearization for small deformations (lTPM) -- whereafter, due to the coupled nature of the problem, the PDE system is still non-linear (see e.g [1]) -- or usage of the Biots equations offers outways. Clearly, this limits the applicability of the models. For the development of general and robust solution strategies for non-linear poroelastic problems, the close collaboration of applied mathematicians and engineers is essential. Within the first part of this talk (Type 1, Presentation in pairs), a novel least-squares formulation for the Biot problem is presented from a mathematical point of view. Robustness within the incompressible limit is achieved. The extension of this formulation to the lTPM results in a reliable and efficient error estimator for this non-linear problem. Especially within the engineering community, many existing code frameworks are based on classical finite-element approximations, using a displacement-pressure formulation. Therefore, the second part of this talk will take an engineering perspective on the construction of adaptive solution strategies for such approximations. By applying reconstruction techniques following [2], the previously discussed least-squares functional can be evaluated and serves as adaption criterion. References: [1] Bertrand F., Brodbeck M. and Ricken T. On robust discretization methods for poroelastic problems: Numerical examples and counter-examples. EXCO (2022) 2 [2] Bertrand F. and Starke G. A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem. Comput. Math. with Appl. (2021) 91: 3-16