  We review and compare theoretically and phenomenologically a number of
possible family symmetries, which when combined with unification, could be
important in explaining quark, lepton and neutrino masses and mixings,
providing new results in several cases. Theoretical possibilities include
Abelian or non-Abelian, symmetric or non symmetric Yukawa matrices, Grand
Unification or not. Our main focus is on anomaly-free U(1) family symmetry
combined with SU(5) unification, although we also discuss other possibilities.
We provide a detailed phenomenological fit of the fermion masses and mixings
for several examples, and discuss the supersymmetric flavour issues in such
theories, including a detailed analysis of lepton flavour violation. We show
that it is not possible to quantitatively and decisively discriminate between
these different theoretical possibilities at the present time.
