We theoretically and experimentally investigate the impact of pore space structure, wettability, and surface roughness on the displacement front, trapping, and sweeping efficiency at low capillary numbers. The microstructure of (i) 2D geologically-realistic media (2D natural sand and sandstone), (ii) a topological 3D-2D-transformation (2D sand analog), and (iii) geometrically representative media (Delaunay Triangulation) were studied over a wide range of wettability from water-wet to oil-wet systems provided by using various fluid-pairs. We observed the transition (compact to fractal) in the displacement front caused by local instabilities identified by Cieplak and Robbins. The trapping efficiency of 2D natural microstructures showed a non-monotonous dependency on wettability, whereas a crossover from no trapping to maximal trapping was observed in 2D patterns of circular grains. For the first time, we compared identical experimental microstructures with simulation, capturing the key elements of the invasion process. We demonstrated that corner flows occur particularly in low-porosity media, where the smaller grain-grain distance hindered the corner-flow bridging. These insights could improve the CO2 geological storage and Enhanced Oil Recovery processes.