An aqueous droplet in a solution of lipids in oil acquires a lipid monolayer coat, and two such droplets adhere to form a bilayer at their interface. Networks of droplets have been constructed in this way that function as light sensors, batteries and electrical circuits by using membrane proteins incorporated into the bilayers. However, the droplets have been confined to a bulk oil phase, which precludes direct communication with physiological environments. Further, the networks typically have been assembled manually, which limits their scale and complexity. This thesis addresses these limitations, and thereby enables prospective medical and technological applications for droplet networks. In the first part of the work, defined droplet networks are encapsulated within mm-scale drops of oil in water to form structures called multisomes. The encapsulated droplets adhere to one another and to the surface of the oil drop to form interface bilayers that allow them to communicate with each other and with the surrounding aqueous environment through membrane pores. The contents of the droplets can be released by changing the pH or temperature of the surrounding solution. Multisomes have potential applications in synthetic biology and medicine. In the second part of the work, a three-dimensional printing technique is developed that allows the construction of complex networks of tens of thousands of heterologous droplets ~50 µm in diameter. The droplets form a self-supporting material in bulk oil or water analogous to biological tissue. The mechanical properties of the material are calculated to be similar to those of soft tissues. Membrane proteins can be printed in specific droplets, for example to establish a conductive pathway through an otherwise insulating network. Further, the networks can be programmed by osmolarity gradients to fold into designed shapes. Printed droplet networks can serve as platforms for soft devices, and might be interfaced with living tissues for medical applications.