We here review the current knowledge of lyotropic liquid-crystalline phases having structures based upon periodic three-dimensional packings of discrete inverse micellar aggregates. These have been shown during the last decade to be rather common in lipid systems, particularly in lipid mixtures. The most frequently observed such structure is a cubic phase of crystallographic spacegroup Fd3m. We have previously determined the structure of this inverse micellar cubic phase, both by X-ray diffraction (V. Luzzati, R. Vargas, A. Gulik, P. Mariani, J. M. Seddon and E. Rivas, Biochemistry, 1992, 31, 279) and by freeze fracture electron microscopy (FFEM) (H. Delacroix, T. Gulik-Krzywicki and J. M. Seddon, J. Mol. Biol., 1996, 258, 88), and have determined the effect of pressure on its stability (P. M. Duesing, J. M. Seddon, R. H. Templer and D. A. Mannock, Langmuir, 1997, 13, 265). We have measured the limiting hydration of the Fd3m phase in a number of lipid systems. We have found that electrical conductivity measurements can offer a simple way of distinguishing bicontinuous from discontinuous (inverse micellar) phases. We have also discovered a new optically-isotropic phase in a few lipid systems, at lower hydrations than the Fd3m cubic phase. The X-ray diffraction pattern does not appear to index as cubic, and we assume that this phase consists of a non-cubic complex 3-D packing of inverse micelles. It gives rise to three different fracture planes by FFEM, one of which is identical to the [111] fracture plane of the Fd3m cubic phase, with two different sub-domains with alternating aspects along the [111] direction being present. This implies that the two inverse micellar phases may be related by a restacking transition of planes normal to the cubic [111] direction, analogous to the fcc–hcp restacking transition of hard spheres.