© 2018 Uspekhi Fizicheskikh Nauk, Russian Academy of Sciences. First discovered in 2007, fast radio bursts (FRBs) are highly luminous (10-1-102 Jy), millisecond-scale, highly dispersive single radio pulses whose record high brightness temperatures suggest a nonthermal emission mechanism. As of March 2018, a total of 32 FRBs have been recorded. There is also one repeating source, from which hundreds of bursts have already been detected. The rate of events is estimated to be several thousand per day per sky (disregarding bursts from the repeater), and their isotropic distribution in the sky suggests a likely cosmological origin. While numerous hypotheses have been proposed for FRBs since their discovery, the origin of these transients is not yet known. The most promising models either relate them to burst-type radiation from magnetars (neutron stars powered by the dissipation of their magnetic energy) or consider them analogous to giant pulses from some radio pulsars (strongly magnetized rotating neutron stars). The increasing statistics on the observed bursts and improvements in characterizing the FRB population will allow FRBs to become another tool for probing the intergalactic medium, estimating the cosmological parameters, and testing fundamental physical theories.