AbstractMuch of the function of lipids, as in shortenings, confections, biological membranes, etc., depends on the structures they exhibit, i.e., their crystalline and mesomorphic states. Triglycerides may serve as a point of departure for considering the crystal state of lipids. The three principle cross‐sectional arrangements of long chains‐α, β′ and β‐in which there is kinship to hydrocarbons, offer a major basis for classification. Different crystal forms are rheologically different. Complications in the chain length direction lead to stepped configurations in the methyl planes and to double and triple chain length structures. A detailed consideration of the time‐honored melting point alternation of homologs sheds light on the lipid crystal picture. A startling feature is the catalysis of isomerization by the solid state of diglycerides, with a consequent shift in equilibrium far toward 100% 1,3‐diglyceride. Stepwise reversible transformations, as in hydrocarbons, are documented for high molecular weight 1‐monoglycerides. A common feature, the sharp drop with mixture of stable form melting points, to “expose” metastable forms as stable forms for intermediate compositions is strikingly exhibited by fatty alcohols. The two bases for mesomorphism, or liquid crystal formation, among lipids are discussed: (1) dichotomy between molecular moieties in degree of polarity, as in phospholipids; and (2) dichotomy in molecular geometry as in cholesteryl esters. The former type is associated with three main basic arrangements‐smectic or lamellar, middle or hexagonal (normal and reversed), and viscous isotropic or cubic (normal and reversed). The latter is associated with two main arrangements‐cholesteric (essentially limited to cholesteryl compounds) and smectic. The importance of mesomorphism in consideration of membranes and emulsions is emphasized. Developments in understanding the structures of interfacial lipid states (including monomolecular surface films) and the correspondence of interfacial with bulk states is a matter of great continuing interest.