The solubilization of lipid bilayers by surfactants is accompanied by morphological changes of the bilayer and the emergence of mixed micelles. From a phase equilibrium perspective, the lipid/surfactant/water system is in a two-phase area during the solubilization: a phase containing mixed micelles is in equilibrium with bilayer structures of the lamellar phase. In some cases three phases are present, the single micelle phase replaced by a concentrated and a dilute solution phase. In the case of non-ionic surfactants, the lipid bilayers reach saturation when mixed micelles, often flexible rod-like or thread-like, start to form in the aqueous solution, at a constant chemical potential of the surfactant. The composition of the bilayers also remains fixed during the dissolution. The phase behavior encountered with many charged surfactants is different. The lamellar phase becomes destabilized at a certain content of surfactant in the membrane, and then disintegrates, forming mixed micelles, or a hexagonal phase, or an intermediate phase. Defective bilayer intermediates, such as perforated vesicles, have been found in several systems, mainly with charged surfactants. The perforated membranes, in some systems, go over into thread-like micelles via lace-like structures, often without a clear two-phase region. Intermediates in the form of disks, either micelles or bilayer fragments, have been observed in several cases. Most noteworthy are the planar and circular disks found in systems containing a large fraction of cholesterol in the bilayer. Bile salts are a special class of surfactants that seem to break down the bilayer at low additions. Originally, disk-like mixed micelles were conjectured, with polar membrane lipids building the disk, and the bile salts covering the hydrophobic rim. Later work has shown that flexible cylinders are the dominant intermediates also in these systems, even if the disk-like structures have been re-established as transients in the transformation from mixed micelles to vesicles.