Lipid-based nanostructures are fundamental structures in nature, providing the structural basis of organelles that support localised intracellular and extracellular biochemical functions within living organisms. These structures have inspired a range of biotechnological developments, including nanoparticulate formulations for enhanced therapeutic delivery. Lipids can self-assemble into a broad array of different nanostructures dependent on their molecular shape, which gives rise to a preferred interfacial curvature in their assembled supramolecular state. This rich lipid polymorphism gives rise to a broad range of tuneability in the properties of lipid-based formulations. Curved 3D membrane networks known as cubosomes have been of particular recent interest; their high interfacial surface area gives a high capacity for drug loading and interfacial chemical processes within an individual nanoparticle. Therefore cubosomes are of broad interest within nanomedicine and bottom-up approaches to synthetic biology through the design of artificial cells. The internal structure of cubosomes consists of highly curved lipid bilayers being draped around a periodic minimal surface creating two distinct continuous 3D-networks of water channels (Fig. ).