Generation of membrane curvature is compulsory for some of the most sophisticated forms of intercellular communication. Cells bend their membranes into spherical vesicles and thin, finger-like projections to package and deliver complex messages to other cells during diverse developmental and physiological programs. I will discuss how cells exploit basic principles of polymer science to bend the plasma membrane into the highly curved forms required for these advanced communication structures. Like a compressed gas hovering over the membrane, flexible biopolymers anchored on the cell surface generate a pressure that eases the formation of curved membrane features. I also will discuss our progress in leveraging the tools of synthetic biology to achieve programmable control over plasma membrane shapes and, ultimately, desired modes of intercellular communication. Namely, we design and genetically encode new types of cell surface biopolymers that alter cellular behavior in a predictable manner. Additional applications of our encoded biopolymer technology range from anti-stick coatings on mammalian cells for reduced aggregation in bioreactors to new types of bio-lubricants for joint disease, dry eye syndrome, and other biomedical challenges.