Lipid metabolism is accompanied by the solubilization of lipid bilayer membranes by bile salts. We use Brownian dynamics simulations to study the solubilization of model membranes and vesicles by sodium cholate. The solubilization pathways of small and large vesicles are found to be different. Both results for small and large vesicles can be compared with predictions of a macroscopic theoretical description. The line tension of bilayer edges is an important parameter in the solubilization process. We propose a simple method to determine the line tension by analyzing the shape fluctuations of planar membrane patches. Macroscopic mechanical models provide a reasonable explanation for processes observed when a spherical vesicle consisting of lipids and adsorbed bile salt molecules is transformed into mixed lipid-bile salt micelles.