Shell model spectroscopy far from stability

I will discuss the impact of the research on exotic nuclei carried out at ISOLDE and later on, following its impulse, in many laboratories worldwide, in our present knowledge of the nuclear dynamics. I will put particular emphasis on the occurrence of islands of inversion (IoI) at several magic numbers for the neutrons, far from stability. I will also discuss the appearance of new local shell closures in the calcium and silicon isotopic chains, and qualify their status as new doubly magic nuclei.