Protein molecules in solution or in protein crystals are characterized by rather well-defined structures in which α-helical regions, β-pleated sheets, etc., are the key features. Likewise, the double helix of nucleic acids has almost become the trademark of molecular biology as such. By contrast, the structural analysis of lipids has progressed at a relatively slow pace. The early X-ray diffraction studies by V. Luzzati and others firmly established the fact that the lipids in biological membranes are predominantly organized in bilayer structures (Luzzati, 1968). V. Luzzati was also the first to emphasize the liquid-like conformation of the hydrocarbon chains, similar to that of a liquid paraffin, yet with the average orientation of the chains perpendicular to the lipid–water interface. This liquid–crystalline bilayer is generally observed in lipid–water systems at sufficiently high temperature and water content, as well as in intact biological membranes under physiological conditions (Luzzati & Husson, 1962; Luzzati, 1968; Tardieu, Luzzati & Reman, 1973; Engelman, 1971; Shipley, 1973). In combination with thermodynamic and other spectroscopic observations these investigations culminated in the formulation of the fluid mosaic model of biological membranes (cf. Singer, 1971). However, within the limits of this model the exact nature of lipid conformation and dynamics was immaterial, the lipids were simply pictured as circles with two squiggly lines representing the polar head group and the fatty acyl chains, respectively. No attempt was made to incorporate the well-established chemical structure into this picture. Similarly, membrane proteins were visualized as smooth rotational ellipsoids disregarding the possibility that protruding amino acid side-chains and irregularities of the backbone folding may create a rather rugged protein surface.