This article discusses theoretical consequences of quantum-statistical representations of logarithm of isotopic reduced partition function ratio (ln beta). Among the effects being under consideration are the localization of equilibrium isotope effect on the molecular structural elements in the vicinity of the site of isotopic substitution, distribution of increments of ln beta, relationship between ln beta values for the substitution of different atoms, and the influence of anharmonicity. The review also presents the phenomenological analysis of ln beta for more than 2000 compounds as well as the classification of equilibrium isotope effects according to the causes of their appearance. Methods for the quantitative statistical estimation of the maximum possible isotope separation factors and criteria for the purposeful search for chemical exchange systems applicable for the practical separation of isotopes are also given.