Three advanced nuclear power systems use liquid salt coolants that generate tritium and thus face the common challenges of containing and capturing tritium to prevent its release to the environment. The fluoride salt-cooled high-temperature reactor (FHR) uses clean fluoride salt coolants and the same graphite-matrix coated-particle fuel as high-temperature gas-cooled reactors. Molten salt reactors (MSRs) dissolve the fuel in a fluoride or chloride salt with release of fission product tritium into the salt. In most FHR and MSR systems, the baseline salts contain lithium where isotopically separated 7 Li is proposed to minimize tritium production from neutron interactions with the salt. The Chinese Academy of Sciences plans to start operation of a 2-MW(thermal) molten salt test reactor by 2020. For high-magnetic-field fusion machines, the use of lithium enriched in 6 Li is proposed to maximize tritium generation-the fuel for a fusion machine. Advances in superconductors that enable higher power densities may require the use of molten lithium salts for fusion blankets and as coolants. Recent technical advances in these three reactor classes have resulted in increased government and private interest and the beginning of a coordinated effort to address the tritium control challenges in 700°C liquid salt systems. We describe characteristics of salt-cooled fission and fusion machines, the basis for growing interest in these technologies, tritium generation in molten salts, the environment for tritium capture, models for high-temperature tritium transport in salt systems, alternative strategies for tritium control, and ongoing experimental work. Several methods to control tritium appear viable. Limited experimental data are the primary constraint for designing efficient cost-effective methods of tritium control.