Over the past six years (2015)(2016)(2017)(2018)(2019)(2020)(2021), many superconducting hydrides with critical temperatures TC 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 electronphonon interaction, especially when anharmonicity of phonons is taken into account. We investigate 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, and the dependence of Tc on the pressure and the degree of doping. The divergences between the theory and experiment are of interest, especially in the regions of phase stability and in the behavior of the upper critical magnetic fields at low temperatures. We present a retrospective analysis of data of 2015-2021 and describe promising directions for future research of hydride superconductivity.