While significant advances have been achieved with non-living synthetic cells built from the bottom-up, less progress has been made with the fabrication of synthetic tissues built from such cells. Synthetic tissues comprise patterned three-dimensional (3D) collections of communicating compartments. They can include both biological and synthetic parts and may incorporate features that do more than merely mimic nature. 3D-printed materials based on droplet-interface bilayers are the basis of the most advanced synthetic tissues and are being developed for several applications, including the controlled release of therapeutic agents and the repair of damaged organs. Current goals include the ability to manipulate synthetic tissues by remote signaling and the formation of hybrid structures with fabricated or natural living tissues.