Abstract. The theory and phenomenology of light sterile neutrinos at the eV mass scale is reviewed. The reactor, Gallium and LSND anomalies are briefly described and interpreted as indications of the existence of short-baseline oscillations which require the existence of light sterile neutrinos. The global fits of short-baseline oscillation data in 3+1 and 3+2 schemes are discussed, together with the implications for β-decay and neutrinoless double-β decay. The cosmological effects of light sterile neutrinos are briefly reviewed and the implications of existing cosmological data are discussed. The review concludes with a summary of future perspectives.

We present accurate predictions of the effective Majorana mass |m ββ | in neutrinoless double-β decay in the standard case of 3ν mixing and in the case of 3+1 neutrino mixing indicated by the reactor, Gallium and LSND anomalies. We have taken into account the uncertainties of the neutrino mixing parameters determined by oscillation experiments. It is shown that the predictions for |m ββ | in the cases of 3ν and 3+1 mixing are quite different, in agreement with previous discussions in the literature, and that future measurements of neutrinoless double-β decay and of the effective light neutrino mass in β decay or the total mass of the three lightest neutrinos in cosmological experiments may distinguish the 3ν and 3+1 cases if the mass ordering is determined by oscillation experiments. We also present a relatively simple method to determine the minimum value of |m ββ | in the general case of N -neutrino mixing.