Work on surface-enhanced Raman scattering (RS) of light by molecules near a metal surface is reviewed. The experimental conditions for obtaining surface-enhanced Raman scattering spectra in different molecule-metal systems are examined. The basic characteristics and mechanisms of the effect are discussed. Special attention is devoted to applications of the method of surface-enhanced Raman scattering spectroscopy for structural-functional study of biological molecules: DNA, proteins, supramolecular complexes. It is pointed out that the large enhancement of the RS cross section makes it possible to reduce the concentration of the substances under study by three orders of magnitude--down to 10$^8$--10$^9$ M. The short range of the enhancement mechanism in some systems makes it possible to obtain Raman scattering spectra for groups of atoms located directly adjacent to the surface of the metal and thereby to study the topography of biological macromolecules and the kinetics of their behavior at an interface. The prospects for applications of enhanced Raman scattering as a new method of vibrational spectroscopy of biopolymers are discussed.