Efforts to place separation of isotopes, especially by chromatography or column operation, on a theoretical basis are reviewed. Emphasis is placed on fundamental principles and concepts rather than on details of experimental investigations. Theoretical studies fall into two main lines of approach. The first line of approach is characterized by the application of the ion-exchange or extraction theory to isotope separation; historically this approach as a consequence of the fact that the ion-exchange chromatography was applied to practically the isotope separation of elements. The second line of approach is represented by the chemical exchange method which has hitherto been used in two-phase separation. This approach is applied to interprete the experimental results which were obtained on the uranium isotope separation by the reverse frontal technique and on the lithium isotope separation by the band-elution technique. The relation between the two lines of approach is systematized.