A review of several of the available theories of vibrational energy tr
ansfer (VET) in the gas and liquid phases is presented. First the clas
sical theory of gas phase VET mainly due to Landau and Teller, to Jack
son and Mott and to Zener is developed in some detail. Next the Schwar
tz-Slawsky-Herzfeld theory, a framework for analysing VET data based o
n the classical theory, is outlined. Experimental tests of the classic
al theory and theoretical critiques of its assumptions are then descri
bed. Next a brief review of the modern ab-initio quantum approach to g
as phase VET rates, taking as an example the work of Banks, Clary and
Werner, is given. Theories of VET at elevated densities are then discu
ssed. The isolated binary collision model is reviewed and a new molecu
lar approach to the density, temperature and isotope dependences of vi
brational energy relaxation rates, due to Adelman and co-workers, is o
utlined.