Biomembranes play fundamental roles in all living systems to partition cells into subcellular compartments. However, these typically flat membranes may also fold into 3D periodic nanostructures, termed cubic membranes (CM), under certain physiological or pathological conditions. Three types of CM arrangements—gyroid (G), double diamond (D) and primitive (P)—have been identified in multiple cell types, yet their biological function is still obscure. The surfaces describing CM are triply periodic minimal or level surfaces and of great technological potential in crystalline and liquid crystalline materials at various length scales. This review briefly introduces: (1) the characterization of CM nanostructures by transmission electron microscope (TEM), scanning electron microscope (SEM) and EM tomography in biological systems; (2) an update on experimental data describing the role of lipids, proteins and Ca²⁺ on CM formation; (3) the proposed optical and antioxidant properties of CM; (4) the potential applications as a diagnostic biomarker for various human diseases, use of CM-derived lipids as gene delivery vehicles, use of CM as structural antioxidant, and CM-based photonic crystals as versatile light-modulators.