Studying the interactions between heavy hydrogen isotopes and hydride forming metals or intermetallic compounds (IMC) is of importance for both fundamental and applied sciences. These systems offer, for example, the possibility of technical hydrogen isotope separation due to their considerable isotope effects. In addition, quite a lot of problems of hydrogen recovery, hydrogen purification, and tritium storage can be solved. This review deals with theoretical aspects of the interaction of heavy hydrogen isotopes with metals and IMC, and contains detailed information on phase and isotopic equilibrium and of the kinetics of isotope exchange in systems with hydride phases. Numerical data and results from theoretical and experimental studies are presented as well.