Biological membranes consist of fluid bilayers with many lipid and protein components. This fluidity implies a high flexibility that allows the membranes to attain a large variety of different shapes. One important shape parameter is the spontaneous curvature, which describes the asymmetry between the two leaflets of a bilayer and can be changed by adsorption of 'particles' such as ions or proteins from the aqueous phases. Membrane fluidity also implies that the membranes can change their local composition via lateral diffusion and form intramembrane compartments. Two mechanisms for the formation of such compartments can be distinguished: membrane segmentation arising from structured environments and domain formation as a result of phase separation within the membranes. The interplay between these two mechanisms provides a simple and generic explanation for the difficulty to observe phase domains in vivo. Intramembrane domains can form new membrane compartments via budding and tubulation processes. Which of these two processes actually occurs depends on the fluid-elastic properties of the domains, on the adsorption kinetics, and on external constraints arising, e.g., from the osmotic conditions. Vesicles are predicted to unbind from adhesive surfaces via tubulation when the spontaneous curvature of their membranes exceeds a certain threshold value.