This book is the first collection of lipid-membrane research conducted by leading mechanicians and experts in continuum mechanics. It brings the overall intellectual framework afforded by modern continuum mechanics to bear on a host of challenging problems in lipid membrane physics. These include unique and authoritative treatments of differential geometry, shape elasticity, surface flow and diffusion, interleaf membrane friction, phase transitions, electroelasticity and flexoelectricity, and computational modelling. [Chapter] Lipid bilayers are unique soft materials operating in general in the low Reynolds limit. While their shape is predominantly dominated by curvature elasticity as in a solid shell, their in-plane behavior is that of a largely inextensible viscous fluid. Furthermore, lipid membranes are extremely responsive to chemical stimuli. Because in their biological context they are continuously brought out-of-equilibrium mechanically or chemically, it is important to understand their dynamics. Here, we introduce Onsager’s variational principle as a general and transparent modeling tool for lipid bilayer dynamics. We introduce this principle with elementary examples, and then use it to study the sorption of curved proteins on lipid membranes.