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Discrete non‐Abelian Symmetries have been extensively used to reproduce the lepton mixings. In particular, the S 4  group turned out to be suitable to describe predictive mixing patterns, such as the well‐known Tri‐Bimaximal and the Bimaximal schemes, which all represent possible first approximations of the experimental lepton mixing matrix. We review the main application of the S 4  discrete group as a flavour symmetry, first dealing with the formalism and later with the phenomenological implications. In particular, we summarize the main features of flavour models based on S 4 , commenting on their ability in reproducing a reactor angle in agreement with the recent data and on their predictions for lepton flavour violating transitions.

Neutrino mixings and the S 4 discrete flavour symmetry