Many biological lipid membranes are asymmetric: their two leaflets differ in at least one physical observable. The by far best studied case is lipidomic asymmetry, a difference in the lipid composition between the two sides of the bilayer. But once symmetry is broken, even if in just one observable, other observables generally cease to be symmetric, too. In this talk I will discuss one specific example: the difference in lateral mechanical tension between the two leaflets, which I refer to as “differential stress”. Although presently we do not yet have any experimental means to directly measure it, I will give several arguments that not only show why differential stress should be there, but also why it is likely large: it might well be one or two orders of magnitude bigger than typical net cellular membrane tensions. Such large stresses have many consequences for membrane shape and thermodynamics, the inter-leaflet distribution of cholesterol, or the function of transmembrane proteins. I will present a few examples, which might also offer opportunities to indirectly access this observable.