A contemporary review of quantum models of chemical reactions is presented. At low temperatures tunneling prevails over thermally activated transitions and results in non-Arrhenius behavior of the rate constant, which cannot be described in terms of classical transition state theory and requires explicit incorporation of environment dynamics. The correlation between the quantum rate constant and spectral properties of the heat bath and dynamics of intramolecular vibrations is considered. The spectroscopic evidence of tunneling in molecules is also discussed. The theoretical consideration is illustrated by a number of experimental examples.