Glass formers have a comlicated pattern of relaxations. The fast relaxation corresponds to picosecond time scale. The respective light scattering data in glasses and supercooled liquids in giga - and terahertz frequency range are analyzed. The relation of the fast relaxation spectrum to that of the vibrational spectrum of glasses in THz range (so called "boson peak") receives special attention. Mechanisms of the fast relaxation based on the potential energy landscape picture and on the anharmonic interaction of the THz acoustical vibrations are discussed. In time domain, the data on dynamics of supercooled molecular liquids obtained in optical heterodyne detected optical Kerr effect experiments were analyzed. The logarithmic, or close to logarithmic decay of molecular orientational correlations in the time interval ~ 2 ps to 1~10 ns have been observed from high temperature to ~T_c, the mode-coupling theory (MCT) critical temperature. Possible explanations in terms of the higher order glass transition singularities are discussed.