A review with 181 refs. The quant. exptl. uncertainty in the structure of fully hydrated, biol. relevant, fluid (Lα) phase lipid bilayers has been too large to provide a firm base for applications or for comparison with simulations. Many structural methods are reviewed including modern liq. crystallog. of lipid bilayers that deals with the fully developed undulation fluctuations that occur in the Lα phase. These fluctuations degrade the higher order diffraction data in a way that, if unrecognized, leads to erroneous conclusions regarding bilayer structure. Diffraction measurements at high instrumental resoln. provide a measure of these fluctuations. In addn. to providing better structural detn., this opens a new window on interactions between bilayers, so the exptl. detn. of interbilayer interaction parameters is reviewed briefly. We introduce a new structural correction based on fluctuations that has not been included in any previous studies. Updated measurements, such as for the area compressibility modulus, are used to provide adjustments to many of the literature values of structural quantities. Since the gel (Lβ') phase is valuable as a stepping stone for obtaining fluid phase results, a brief review is given of the lower temp. phases. The uncertainty in structural results for lipid bilayers is being reduced and best current values are provided for bilayers of five lipids