  For a long time there were 3 main experimental indications in favor of the
existence of sterile neutrinos: $\bar{\nu_e}$ appearance in the $\bar{\nu_\mu}$
beam in the LSND experiment, $\bar{\nu_e}$ flux deficit in comparison with
theoretical expectations in reactor experiments, and $\nu_e$ deficit in
calibration runs with radioactive sources in the Ga solar neutrino experiments
SAGE and GALEX. All three problems can be explained by the existence of sterile
neutrinos with the mass square difference in the ballpark of $1~\mathrm{eV^2}$.
Recently the MiniBooNE collaboration observed electron (anti)neutrino
appearance in the muon (anti)neutrino beams. The significance of the effect
reaches 6.0$\sigma$ level when combined with the LSND result. Even more
recently the NEUTRINO-4 collaboration claimed the observation of $\bar{\nu_e}$
oscillations to sterile neutrinos with a significance slightly higher than
3$\sigma$. If these results are confirmed, New Physics beyond the Standard
Model would be required. More than 10 experiments are devoted to searches of
sterile neutrinos. Six very short baseline reactor experiments are taking data
just now. We review the present results and perspectives of these experiments.
