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Clathrin-mediated endocytosis (CME) underlies intra- and extracellular material trafficking in eukaryotes, and is essential to protein metabolism, intercellular signaling, membrane remodeling and other cell regulatory processes. Although CME is usually driven by F-actin polymerization, membrane invagination can also occur through unknown actin independent mechanisms. Here, we present evidence that CME is driven by the accumulation of proteins at sites of endocytosis initiation that undergo liquid-liquid phase separation to form viscoelastic droplets. The surfaces of these droplets, bind to the membrane and surrounding cytosol and generate the work required to drive membrane invagination. The proposed mechanism expands the repertoire of functions of membraneless organelles that form via liquid-liquid phase separation to include their ability to do work due to soft interfaces that shape and organize cellular matter.