The problem of neutrino masses in extensions of the Standard Model

We review the problem of neutrino masses and mixings in the context of Grand Unified Theories. After a brief summary of the present experimental status of neutrino physics, we describe how the see-saw mechanism can automatically account for the large atmospheric mixing angle. We provide two specific examples where this possibility is realized by means of a flavour symmetry. We then review in some detail the various severe problems which plague minimal GUT models (like the doublet-triplet splitting and proton-decay) and which force to investigate the possibility of constructing more elaborate but realistic models. We then show an example of a quasi-realistic SUSY SU(5) model which, by exploiting the crucial presence of an abelian flavour symmetry, does not require any fine-tuning and predicts a satisfactory phenomenology with respect to coupling unification, fermion masses and mixings and bounds from proton decay.