Lipid vesicles are macroscopic objects defined by a lipid membrane enclosing an aqueous medium and separating it from the external aqueous medium. The division of space into internal and external compartments is also the basic characteristic of living cells. Lipid vesicles can form spontaneously and as such they may have been one of the important basic structures involved in biogenesis. Lipid vesicles also possess a variety of properties which could have been employed in the further evolvement of biological systems. Here it is argued that the cellular processes which involve changes of membrane conformations have their origin in the general shape behavior of closed lamellar membranes. This notion is based on some general features of the vesicle shape behavior which are the consequence of the layered membrane structure and do not depend on the structural and compositional details of the composing monolayers. One can thus ascribe these features also to prebiotic vesicles, even without knowing from what type of lipids they were made. The two general features of vesicle shape behavior that may be particularly important bases for possible physical mechanisms underlying different cellular processes are the symmetry breaking in vesicle shape transformations and the propensity of lipid vesicles for budding. The occurrence of stable asymmetric vesicle shapes is proposed to represent the mechanical origin of cellular polarity, and through this also of the biological order. Membrane budding is an obligatory step in vesicle fission and fusion processes taking place in cellular membrane trafficking. At the phenomenological level certain aspects of all these processes can be interpreted already on the basis of the understanding of the shape behavior of lipid vesicles. However, lipid vesicles and cellular systems differ in that the processes involving vesicles are in general stochastic, whereas the processes in a cell are based on a complex protein machinery and are in general deterministic. The point is made that some cellular processes, notable examples are cytokinesis, endocytosis and exocytosis, still emerged from the corresponding physical processes occurring also at the level of pure vesicles, but were properly upgraded and became well regulated in the course of evolution