Cells, the primary units of terrestrial life, are complex and highly organized structures able to grow, replicate and evolve. Here we shall present that growth, replication and evolution can also be ascribed to vesicles which on the contrary are simple physico-chemical objects with their aqueous interior separated from the aqueous exterior by a thin membranous boundary. In the lecture we shall first demonstrate that the growth of vesicle membrane may cause that a vesicle changes its shape, in particular that it may form buds. Vesicle shape behavior will be revealed that was predicted by assuming that a vesicle attains the shape which at given vesicle volume, membrane area and transmembrane asymmetry corresponds to the minimum of the membrane bending energy. Classification of vesicle shapes with respect to their symmetry will be presented, together with describing the causes of vesicle budding. Then we shall describe a simple prototype model of vesicle self-reproduction which is based on the assumption that at doubling its size a vesicle must also change its shape into the shape composed of two buds connected by a narrow neck. It will be shown that vesicle self-reproduction can only occur if a condition is satisfied which interrelates the physical properties of the vesicle membrane and the parameters of the vesicle surrounding. It will be argued that this condition may act as the criterion to select between different vesicle populations. Consequent behavior of vesicle populations will be described and compared to the corresponding behavior of populations of cells. It will be shown that the process of vesicle self-reproduction involves the basic characteristics of the cell cycle. An implication will be made that vesicles might have mediated the transition from the nonliving to the living matter.