Horizontal symmetries and weak mixing angles

The motivation to introduce horizontal symmetries into gauge theories of electroweak interactions is discussed. The main steps which lead to natural relations between weak mixing angles and fermion masses are emphasized. Recent work on general classifications of mass matrices for all possible horizontal groups (discrete or continuous) is reviewed. In particular, it is shown that for a left-right symmetric gauge theory with minimal Higgs sector and either four or six quark flavours there is exactly one model that is phenomenologically acceptable and relates mixing angles to quark masses. (author)