Self-assembly of inanimate objects into well-defined 3D structures, such as folded proteins or DNA-origami, remains a mystery. Inspired by biological systems, we design and make droplets stabilized by lipid mixtures and functionalized with cell-cell adhesion proteins or DNA. We discover that lipids phase separate on the droplet surface to create stable and tunable patterns of circular or stripy domains, reminiscent of lipid rafts in cell membranes. These domains carry adhesive proteins or DNA, which drive the specific and reversible binding between droplets to generate large scale structures. For example, we show that these mobile adhesion patches self-assemble linear chains of droplets into compact structures, mimicking protein folding on the mesoscopic scale. These results demonstrate the control of valency, geometry and specificity of droplet bonds to open novel routes to the self-assembly of materials with desired geometries.