Biological and biomimetic membranes are based on lipid bilayers, which consist of two monolayers or leaflets. To avoid bilayer edges, which form when the hydrophobic core of such a bilayer is exposed to the surrounding aqueous solution, a single bilayer closes up into a unilamellar vesicle, thereby separating an interior from an exterior aqueous compartment. Synthetic nanovesicles with a size below 100 nanometers, traditionally called small unilamellar vesicles, have emerged as potent platforms for the delivery of drugs and vaccines. Cellular nanovesicles of a similar size are released from almost every type of living cell. The nanovesicle morphology has been studied by electron microscopy methods but these methods are limited to a single snapshot of each vesicle. Here, we review recent results of molecular dynamics simulations, by which one can monitor and elucidate the spatio-temporal remodeling of individual bilayers and nanovesicles. We emphasize the new concept of leaflet tensions, which control the bilayers’ stability and instability, the transition rates of lipid flip-flops between the two leaflets, the shape transformations of nanovesicles, the engulfment and endocytosis of condensate droplets and rigid nanoparticles, as well as nanovesicle adhesion and fusion. To actually compute the leaflet tensions, one has to determine the bilayer’s midsurface, which represents the average position of the interface between the two leaflets. Two particularly useful methods to determine this midsurface are based on the density profile of the hydrophobic lipid chains and on the molecular volumes.