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Ordered amphiphile self-assembly materials with a tunable three-dimensional (3D) nanostructure are of fundamental interest, and crucial for progressing several biological and biomedical applications, including in meso membrane protein crystallization, as drug and medical contrast agent delivery vehicles, and as biosensors and biofuel cells. In binary systems consisting of an amphiphile and a solvent, the ability to tune the 3D cubic phase nanostructure, lipid bilayer properties and the lipid mesophase is limited. A move beyond the binary compositional space is therefore required for efficient engineering of the required material properties. In this critical review, the phase transitions upon encapsulation of more than 130 amphiphilic and soluble additives into the bicontinuous lipidic cubic phase under excess hydration are summarized. The data are interpreted using geometric considerations, interfacial curvature …