Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)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 beta-decay and neutrinoless double-beta 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.433research grant Theoretical Astroparticle Physics under the program PRIN - Ministero dell'Istruzione, Universita e della Ricerca (MIUR) [2012CPPYP7]National Natural Science Foundation of China [11135009, 11305193]Tianjin Science Technology Research Funds of China [12JCYBJC3200]RFBR (Russia) [15-52-53112]NSFC (China) [11511130016]Sao Paulo Research Foundation (FAPESP) [2013/02518-7, 2014/23980-3]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)