The very formal structure of quantum mechanics implies the loss of individuality of physical systems and it requires to look at the Universe as an unbroken whole. The main reason for which, within such a theory, one must renounce to a clear identification of the parts and the whole is the superposition principle which stays at the basis of the theory. It implies, as well known, the phenomenon of entanglement which, in the most extreme case, entails that the constituents of a composite system do not possess any objective property; only the system as a whole, when it is isolated, has some properties. Another source of difficulties derives from the symmetry requests that the theory imposes in the case of systems containing identical constituents. We discuss these points in detail and we outline recent proposals yielding a consistent solution to the problems arising from the entanglement between a microsystem and a macrosystem which unavoidably occurs in a measurement process. In particular we take into account the so called "collapse" theories which embody a mechanism forbidding, at an appropriate level, the persistence of superpositions and, as a consequence, lead, in general, to the emergence of precise individual properties for macroscopic systems. We then pass to a critical analysis of the difficulties related to the identity of the constituents. We stress that various misunderstandings characterize the treatment of this problem and we make fully clear how one has to deal with the very concept of entangled systems when identical constituents are involved. The ensuing picture should make clear to which extent one can still consistently ground the distinction between the parts and the whole in a genuinely quantum context.