A review is given of the investigations of lasers in which the amplifying medium is a rapidly recombining (supercooled in respect to free electrons) dense plasma. Efficient amplification of visible and ultraviolet radiation is possible in a plasma with a free-electron density N$_e$= 10$^{13}$--10$^{18}$ cm$^{-3}$ and an electron temperature T$_e$=0.05--2 eV. At short wavelengths and high energies, the plasma lasers have important advantages over the conventional gas lasers in which the active medium is a gas-discharge overheated plasma which is being ionized. The purpose of the review is to identify the developing trends in the investigations of plasma lasers. An analysis is made of the recombination mechanisms of population inversion of atomic, ionic, and molecular levels, of the methods of producing a supercooled plasma, and of the characteristics of different variants of plasma lasers. The general theoretical ideas are illustrated by numerical calculations and experimental results.