The coupling between fluids and the deformation of porous materials, referred to as poromechanics, is an important component of many engineering applications, see [1]. The robustness and reliability of the resulting numerical approximations are therefore an essential task. In this presentation of type 1, presentation in pairs, the second author will therefore present how different scales often can be taken into account from a discretization point of view. The focus will be on the robustness of the error estimates with respect to the system parameters. This however leads to complex structures and the first author will therefore discuss how monolithic solvers can meet with difficulties, and present recent iterative splitting schemes that allow independent and tailored simulators for each subproblem, see [2]. Examining the new numerical methods through these distinct lenses is likely to spark rigorous debates about the advantages and disadvantages of approaches that prioritize one aspect over another. This will be particularly important in discussing poromechanical simulations adaptivity driven by reliable and efficient a posteriori error estimates. REFERENCES [1] Fleurianne Bertrand, Alexandre Ern and Florin Adrian Radu, Robust and reliable finite element methods in poromechanics. Computers and Mathematics with Applications, Vol. 91, pp. 1–2, 2021. [2] Both, Jakub Wiktor and Borregales, Manuel and Nordbotten, Jan Martin and Kumar, Kundan and Radu, Florin Adrian, Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters, Vol. 68, pp. 101–108, 2017.