We review neutrino oscillation physics, including the determination of mass splittings and mixings from current solar, atmospheric, reactor and accelerator neutrino data. A brief discussion is given of cosmological and astrophysical implications. Non-oscillation phenomena such as neutrinoless double beta decay would, if discovered, probe the absolute scale of neutrino mass and also reveal their Majorana nature. Non-oscillation descriptions in terms of spin-flavor precession (SFP) and non-standard neutrino interactions (NSI) currently provide an excellent fit of the solar data. However they are at odds with the first results from the KamLAND experiment which imply that, despite their theoretical interest, non-standard mechanisms can only play a sub-leading role in the solar neutrino anomaly. Accepting the LMA-MSW solution, one can use the current solar neutrino data to place important restrictions on non-standard neutrino properties, such as neutrino magnetic moments. Both solar and atmospheric neutrino data can also be used to place constraints on neutrino instability as well as the more exotic possibility of CPT and Lorentz Violation. Weillustrate the potential of future data from experiments such as KamLAND, Borexino and the upcoming neutrino factories in constraining non-standard neutrino properties.