Membrane curvature is required for many cellular processes, from assembly of highly curved trafficking vesicles to extension of needle-like filopodia. Consequently, defects in membrane curvature play a role in most human diseases, including altered recycling of receptors in cancer and diabetes, targeting of filopodia by pathogens, and hijacking of vesicle traffic during virus replication. Therefore, understanding the basic molecular mechanisms that drive membrane remodeling is essential to our knowledge of cellular physiology and human disease. Research on membrane curvature has primarily focused on individual protein domains with specialized structures, such as crescent-shaped scaffolds and wedge-like amphipathic insertions. While this work has provided invaluable insights, it overlooks two essential elements. First, most membrane remodeling proteins contain large intrinsically disordered domains in addition to structured domains. And second these disordered domains drive assembly of large, multi-valent protein networks. Recent work in our group supports the hypothesis that disordered protein networks are essential drivers of membrane remodeling in the cell. Specifically, using clathrin-mediated endocytosis as a model pathway, we have shown that intrinsically disordered domains generate steric pressure at membrane surfaces. This pressure provides a surprisingly potent driving force for membrane bending, especially when coupled synergistically to the contributions of structured domains. Additionally, we have recently found that disordered domains within endocytic proteins drive assembly of liquid-like protein networks which efficiently initiate endocytosis. Importantly, this liquid-like behavior has the potential to resolve a long-standing paradox by explaining how curved membrane structures can be simultaneously highly interconnected, yet dynamic and flexible.