A number of anomalous results in short-baseline oscillation may hint at the existence of one or more light sterile neutrino states in the eV mass range and have triggered a wave of new experimental efforts to search for a definite signature of oscillations between active and sterile neutrino states. The present paper aims to provide a comprehensive review on the status of light sterile neutrino searches in mid-2019: we discuss not only the basic experimental approaches and sensitivities of reactor, source, atmospheric, and accelerator neutrino oscillation experiments but also the complementary bounds arising from direct neutrino mass experiments and cosmological observations. Moreover, we review current results from global oscillation analyses that include the constraints set by running reactor and atmospheric neutrino experiments. They permit to set tighter bounds on the active-sterile oscillation parameters but as yet are not able to provide a definite conclusion on the existence of eV-scale sterile neutrinos.