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Biomembranes and vesicles cover a wide range of length scales. Indeed, small nanovesicles have a diameter of a few tens of nanometers whereas giant vesicles can have diameters up to hundreds of micrometers. The remodeling of giant vesicles on the micron scale can be observed by light microscopy and understood by the theory of curvature elasticity, which represents a top-down approach. The theory predicts the formation of multispherical shapes as recently observed experimentally. On the nanometer scale, much insight has been obtained via coarse-grained molecular dynamics simulations of nanovesicles, which provides a bottom-up approach based on the lipid numbers assembled in the two bilayer leaflets and the resulting leaflet tensions. The remodeling processes discussed here include the shape transformations of vesicles, their morphological responses to the adhesion of condensate droplets, the instabilities of lipid bilayers and nanovesicles, as well as the topological transformations of vesicles by membrane fission and fusion. The latter processes determine the complex topology of the endoplasmic reticulum.