  Over the past six years (2015-2021), many superconducting hydrides with
critical temperatures $T_{C}$ up to 250 K, which are currently record highs,
have been discovered. Now we can already say that a special field of
superconductivity has developed. This is hydride superconductivity at ultrahigh
pressures. For the most part, the properties of superhydrides are well
described by the Migdal-Eliashberg theory of strong electron-phonon
interaction, especially when anharmonicity of phonons is taken into account.
The isotope effect, the effect of the magnetic field (up to 60-70 T) on the
critical temperature and critical current in the hydride samples, the
dependence of $T_{C}$ on the pressure and degree of doping were investigated.
The divergences between the theory and experiment are of interest, especially
in the field of phase stability and in the behavior of the upper critical
magnetic fields at low temperatures. This article presents a retrospective
analysis of data of 2015-2021 and describes promising directions for future
research of hydride superconductivity.
