Isotope effects in pure isotope systems are reviewed in the first part of this paper. Both the solubility and the mobility of hydrogen isotopes in metals and alloys are considered. The local mode vibrations of the hydrogen isotopes are identified as the origin of isotope effects and are discussed with respect to octahedral and tetrahedral interstitial positions. Deviations from cubic symmetry are briefly mentioned in connection with interstices in group Vb metals, intermetallic compounds and amorphous metals. Isotope effects in hydrogen mobility are shown to be qualitatively explained by the transition state theory. However, the detailed description given by this theory is unsatisfactory because tunnelling corrections and lattice dynamics are not taken into consideration. Mixed isotope systems are discussed in the second part of this paper with particular emphasis on tracer techniques such as tritium tracer exchange and diffusion. The basic thermodynamic expressions for the equilibrium separation factor are given and the ways in which they are related to local mode frequencies are discussed. It is shown that the tracer exchange technique can be used to probe surface hydrogen states which affect both the separation factor and the exchange kinetics. The tritium tracer diffusion technique is briefly explained. A theoretical treatment of the diffusion of a tracer isotope mixture in the presence of traps is described. This method is used to determine 1. (i) the trap binding energy and the trap binding entropy, 2. (ii) the protium-tritium separation factor for trap sites and interstitial sites and 3. (iii) the trap concentration in cold-rolled palladium. It is shown that dislocations act as traps in this material. Finally some practical aspects of the separation of isotopes by permeation techniques and the prediction of large isotope effects are discussed.