  We provide a review on the physics associated with phase transitions in which
continuous scale invariance is broken into discrete scale invariance. The rich
features of this transition characterized by the abrupt formation of a
geometric ladder of eigenstates, low energy universality without fixed points,
scale anomalies and Berezinskii-Kosterlitz-Thouless scaling is described. The
important role of this transition in various celebrated single and many body
quantum systems is discussed along with recent experimental realizations.
Particular focus is devoted to a recent realization in graphene.
