The prediction of transport properties in porous media is of significant importance in different fields and applications, for example geomaterials, concrete or Proton Exchange Membrane electrolyzers. As the Direct Numerical Simulation of the porous structure is computationally very costly, the derivation of the macroscopic response can be calculated by applying computational homogenization methods. In this presentation, a general formulation and derivation for this class of problems will be introduced. Subsequently, the theoretical framework is applied to two distinct applications. The first application is related to Engineered Cementitious Composites (ECCs). These are a class of concrete construction materials reinforced with short fibers that possess the ability to self-heal fractures. We investigate this process by analyzing µ-XRCT (micro X-Ray Computed Tomography) scans of fractures in real ECC samples [1], which serve as calibration and validation data for numerical simulations. We perform a dimensional reduction by means of Variational Multiscale Method and apply Variational Consistent Dimensional Reduction to characterize the effective transport properties of the cracked material at different stages of healing. The second application features Proton Exchange Membrane electrolyzers. During the assembly of electrolysis cells, thin Catalyst Layers (CL) with sub-micron pore size are compressed between Porous Transport Layers (PTL) with much larger pore size, resulting in large localized deformations of the CL pore space [2]. We investigate the influence of this deformation on effective transport properties. Numerically constructed Representative Volume Elements (RVE) are used to represent the CL microscale. Based on this, a two-scale formulation using Variationally Consistent Homogenization (VCH) is derived. A numerical study is performed on a set of sample RVEs to obtain effective ionic and hydraulic conductivities. References: [1] Buegger, U., Tofeti-Lima, T., and Jänicke, R. Analysis of the self-healing capacity of ECCs with high levels of cement replacement by limestone calcined clay cements (LC3), based on micro X-ray computed tomography (µXRCT). In: MATEC Web of Conferences. Vol. 409. EDP Sciences (2025). [2] Ferner, K.J. et al. Morphological analysis of iridium oxide anode catalyst layers for proton exchange membrane water electrolysis using high-resolution imaging. In: Int. J. Hydrogen Energy. Vol. 59, 176-186 (2024).