The quantitative experimental uncertainty in the structure of fully hydrated, biologically relevant, fluid (L(alpha)) 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 liquid crystallography of lipid bilayers that deals with the fully developed undulation fluctuations that occur in the L(alpha) 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 resolution provide a measure of these fluctuations. In addition to providing better structural determination, this opens a new window on interactions between bilayers, so the experimental determination 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 (L(beta)') phase is valuable as a stepping stone for obtaining fluid phase results, a brief review is given of the lower temperature phases. The uncertainty in structural results for lipid bilayers is being reduced and best current values are provided for bilayers of five lipids.