We consider the problem of trying to understand the recently measured neutrino data simultaneously with understanding the heirarchical form of quark and charged lepton Yukawa matrices. We summarise the data that a sucessful model of neutrino mass must predict, and then move on to attempting to do so in the context of spontaneously broken `family symmetries. We consider first an abelian U(1) family symmetry, which appears in the context of a type I string model. Then we consider a model based on a non-abelian SU(3)_F, which is the maximal family group consitent with an SO(10) GUT. In this case the symmetry is more constraining, and is examined in the context of SUSY field theory.