Symmetry, in the sense of invariance with respect of a transformation group, is a central notion in contemporary physics. A symmetry can be exact or broken. This paper considers the nature and significance of symmetry breaking in physical theories, with a special focus on its heuristic role. In particular, starting with the seminal analysis by Pierre Curie in 1894 of the significance of symmetry breaking with respect to physical phenomena, the paper discusses whether, and to which extent, it is possible to generalize Curie's conclusions (in particular, the so-called “Curie's principle”) to the more general and interesting case where symmetry is considered with respect to the physical laws.