The remodeling of cell membranes is fundamental to cell biology and is governed by protein-lipid interactions. This talk will consider two systems. The ESCRT proteins sever the narrow membrane necks that are forced in multivesicular endosome biogenesis, viral budding, cytokinesis, and many other pathways. The ESCRTs are unique in catalyzing reverse-topology scission from the inner face of the membrane neck. We have encapsulated the ESCRTs within giant vesicles and reconstituted scission, revealing mechanistic insights into this unusual process. Autophagy is a conserved mechanism that is essential for cell survival in starvation and for cellular homeostasis. Autophagy proceeds by the engulfment of bulk cytosol and organelles by a cup-shaped double membrane sheet known as the phagophore, which matures into the autophagosome. The Atg1/ULK1 kinase complex appears to have a central role in creating the cup shape of the early phagophore. We will describe how the structure of subunits of this complex could promote formation of the unique curvature needed to create phagophores.