A vast majority of cellular processes take root at the surface of biological membranes. By providing a two-dimensional platform with limited diffusion, membranes are, by nature, perfect devices to concentrate signaling and metabolic components. As such, membranes often act as "key processors" of cellular information. Biological membranes are highly dynamic and deformable and can be shaped into curved, tubular, or flat conformations, resulting in differentiated biophysical properties. At membrane contact sites, membranes from adjacent organelles come together into a unique 3D configuration, forming functionally distinct microdomains, which facilitate spatially regulated functions, such as organelle communication. Here, we describe the diversity of geometries of contact site-forming membranes in different eukaryotic organisms and explore the emerging notion that their shape, 3D architecture, and remodeling jointly define their cellular activity. The review also provides selected examples highlighting changes in membrane contact site architecture acting as rapid and local responses to cellular perturbations, and summarizes our current understanding of how those structural changes confer functional specificity to those cellular territories.