Light sterile neutrinos**This review is dedicated to the memory of Hai-Wei Long, our dear friend and collaborator, who passed away on 29 May 2015. He was an exceptionally kind person and an enthusiastic physicist. We deeply miss him.

Abstract

The theory and phenomenology of light sterile neutrinos at the eV mass scale is reviewed. The reactor, gallium and Liquid Scintillator Neutrino Detector 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.