Many attempts have been made to interpret the existence of the quark-lepton families and the pattern of their mixing in terms of various family symmetries – discrete or continuous, global or local. Among them, the abelian U ( 1 ) F and non-abelian S U ( 2 ) F and S U ( 3 ) F family symmetries seem to be most interesting. They provide some guidance to the mass matrices for families of quarks and leptons, leading to relationships between their masses and mixing parameters. In the framework of the supersymmetric Standard Model, such a family symmetry should at the same time provide an almost uniform mass spectrum for superpartners, with a high degree of the family flavor conservation, that makes its existence even more necessary in the SUSY case.