Spontaneous symmetry breaking is a core concept with applications widely span multiple fields such as high energy physics, cosmology and condensed matter physics. The idea is heavily implemented in the remarkable Landau-Ginzburg paradigm used to classify numerous phases of matter and their phase transitions according to the symmetries they represent/break. In this informal talk, I will introduce briefly such a paradigm and discuss a number of physical systems that depart from it. These include topologically ordered states such as fractional quantum Hall systems and quantum spin liquids in addition to other topological phases of matter which are a cornerstone of modern condensed matter physics.