The discovery of the morphology-transport relationships for chromatographic media (packed beds, monoliths, confined pillar structures) belongs to the remaining major challenges in separation science.Because these fundamental relationships can be neither inferred from visual inspection nor from two-dimensional simulations, the coupled three-dimensional physical reconstruction and/or computer-generation together with a detailed morphological analysis and three-dimensional modeling of transport phenomena provides the only direct as well as the most realistic approach to understand and optimize current and future chromatographic supports.In this presentation I will provide a brief summary of these challenges and present our latest progress at the following levels: (1) Computer-generation of bulk and confined packed beds allows the systematic investigation of individual parameters, such as the particle size distribution, particle porosity, the bed porosity, and the effect of the confinement [1-3].These studies are complemented by the physical reconstruction of real packed and monolithic beds, which demonstrate numerous features coupled with the packing process or monolith synthesis that are under the control of the experimentalist [4-6].(2) Once computer-generated and/or physically reconstructed packed-bed and monolith morphologies are available, they are analyzed with statistical methods to derive appropriate and unique structural descriptors for mass transport (diffusion, dispersion) [4-8].Spatial tessellation schemes proved to be particularly useful in this regard and allowed us to deduce strong correlations for the degree of local and packing-scale heterogeneities with diffusion and dispersion [7,8].