We discuss the shape formation and shape transitions of simple bilayer vesicles in context with their role in biology. In the first part several classes of shape changes of vesicles of one lipid component are described and it is shown that these can be explained in terms of the bending energy concept in particular augmented by the bilayer coupling hypothesis. In the second

part shape changes and vesicle fission of vesicles composed of membranes of lipid mixtures are reported. These are explained in terms of coupling between local curvature and phase separation.