This is a review article about neutrino mass models, particularly see-saw models involving three active neutrinos that are capable of describing both the atmospheric neutrino oscillation data and the large mixing angle (LMA) MSW solar solution, which is now uniquely specified by recent data. We briefly review the current experimental status, show how to parametrize and construct the neutrino mixing matrix, and present the leading order neutrino Majorana mass matrices. We then introduce the see-saw mechanism and discuss a natural application of it to current data using the sequential dominance mechanism, which we compare with an early proposal for obtaining LMAs. We show how both the Standard Model and the Minimal Supersymmetric Standard Model may be extended to incorporate the see-saw mechanism and show how the latter case leads to the expectation of lepton flavour violation. The see-saw mechanism motivates models with additional symmetries such as unification and family symmetry models, and we tabulate some possible models before focusing on two particular examples based on SO(10) grand unification and either U(1) or SU(3) family symmetry as specific examples. This review contains extensive appendices that include techniques for analytically diagonalizing different types of mass matrices involving two LMAs and one small mixing angle, to leading order in the small mixing angle.