Membrane budding is a key step in vesicular transport, multivesicular body biogenesis, and enveloped virus release. These events range from those that are primarily protein driven, such as the formation of coated vesicles, to those that are primarily lipid driven, such as microdomain-dependent biogenesis of multivesicular bodies. Other types of budding reside in the middle of this spectrum, including caveolae biogenesis, HIV-1 budding, and ESCRT-catalyzed multivesicular body formation. Some of these latter events involve budding away from cytosol, and this unusual topology involves unique mechanisms. This Review discusses progress toward understanding the structural and energetic bases of these different membrane-budding paradigms.