Biological membranes undergo constant remodeling by membrane fission and fusion to change their shape and to exchange material between subcellular compartments. During clathrin-mediated endocytosis, the dynamic assembly and disassembly of protein scaffolds comprising members of the bin-amphiphysin-rvs (BAR) domain protein superfamily constrain the membrane into distinct shapes as the pathway progresses toward fission by the GTPase dynamin. In this Review, we discuss how BAR domain protein assembly and disassembly are controlled in space and time and which structural and biochemical features allow the tight regulation of their shape and function to enable dynamin-mediated membrane fission.