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We review and compare theoretically and phenomenologically a number ofpossible family symmetries, which when combined with unification, could beimportant in explaining quark, lepton and neutrino masses and mixings,providing new results in several cases. Theoretical possibilities includeAbelian or non-Abelian, symmetric or non symmetric Yukawa matrices, GrandUnification or not. Our main focus is on anomaly-free U(1) family symmetrycombined with SU(5) unification, although we also discuss other possibilities.We provide a detailed phenomenological fit of the fermion masses and mixingsfor several examples, and discuss the supersymmetric flavour issues in suchtheories, including a detailed analysis of lepton flavour violation. We showthat it is not possible to quantitatively and decisively discriminate betweenthese different theoretical possibilities at the present time.Comment: 75 pages, 4 figure

Study of theory and phenomenology of some classes of family symmetry and unification models