Cellular membranes belong to the most vital yet least understood biomaterials of live
matter. For instance, its biomechanical requirements substantially vary across species
and subcellular sites, raising the question how membranes manage to adjust to such
dramatic changes. Central to its adaptability at the cell surface is the interplay
between the plasma membrane and the adjacent cell cortex, forming an adaptive composite
material that dynamically adjusts its mechanical properties. Using a hypothetical
composite material, we identify core challenges, and discuss how cellular membranes
solved these tasks. We further muse how pathological changes in material properties
affect membrane mechanics and cell function, before closing with open questions and
future challenges arising when studying cellular membranes.