Multiphase flow, deformation, and hydrodynamic transport in complex permeable media are key processes across different scientific and technological disciplines. Uncovering the underlying mechanisms that control theses processes is essential to understand a wide array of natural and engineered systems, from geological energy storage and production to biological media, and fuel cell technologies. Yet our understanding of porous media systems is often hampered by the multiscale spatial heterogeneity that is intrinsic to industrial, biological, and geological porous materials. Hysteresis and memory-dependent dynamics, which arise from small-scale non-equilibrium phenomena, challenge the current continuum theories of multiphase flow and transport through deformable media. Thus, the main objective of HydroPore is to uncover and systematically quantify the mechanisms and laws that govern multiphase flow, mechanical deformation and hydrodynamic transport in permeable media, from the pore to the regional scales. To achieve this ambitious goal, HydroPore proposes a multidisciplinary and integrated research strategy that combines a new theoretical upscaling framework with novel experimental protocols and cutting-edge numerical simulation techniques.