Abstract: I will revisit some basic elements of our present view of the nuclear spectroscopy related to the description of nuclear collectivity in the laboratory frame. Using the Kumar invariants, I will discuss the meaning and limitations of the concept of nuclear shape. Some unexpected results arise which are at odds with the common lore of the community. Next, I will discuss the physics of the Islands of Inversion (Deformation) in the framework of SM-CI calculations within a SU(3)-like heuristic. I will argue that shape coexistence in neutron rich doubly magic nuclei is the portal to the IoI’s at N=20, 40, and 50. Finally I will mention recent developments of beyond mean-field techniques in large SM valence spaces, that show promises to overcome the dimensionality barriers of the full fledged SM CI calculations.