The disposal of spent nuclear fuel and high-level radioactive waste in the subsurface represents one of the greatest challenges for the geosciences. Most disposal strategies rely on a multiple barrier system, consisting of both natural and engineered materials, to prevent or delay the contact of groundwater with the waste and radionuclide release to the environment. Reactive transport models have been central to understanding and assessing how thermal, hydrological, and geochemical processes are coupled in these containment barriers, which are expected to experience a range of temperatures and geochemical conditions, yet, must maintain their integrity for millions of years.