One of the most interesting developments in low energy nuclear structure in recent years is a new perspective on structural and shape evolution, as a function of N and Z. Much of this renewed interest has been generated by discoveries of phase transitional behavior at low energies in finite nuclei and the proposal and validation of the idea of critical point symmetries. Beyond this, the subject embraces the concepts of dynamical symmetries, Landau theory, a new mapping of structural trajectories for a wide variety of nuclei, and order and chaos in nuclear spectra. In this short overview, we will focus on even–even nuclei although fascinating applications to odd–even nuclei, exploiting the concept of nuclear supersymmetry, have recently been made.