Neutrino oscillations have become well-known phenomena; the measurements of neutrino mixing angles and mass squared differences are continuously improving. Future oscillation experiments will eventually determine the remaining unknown neutrino parameters, namely, the mass ordering, normal or inverted, and the CP-violating phase. On the other hand, the absolute mass scale of neutrinos could be probed by cosmological observations, single beta decay as well as by neutrinoless double beta decay experiments. Furthermore, the last one may shed light on the nature of neutrinos, Dirac or Majorana, by measuring the effective Majorana mass of neutrinos. However, the neutrino mass generation mechanism remains unknown. A well-motivated phenomenological approach to search for new physics, in the neutrino sector, is that of non-standard interactions. In this short review, the current constraints in this picture, as well as the perspectives from future experiments, are discussed.