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Materials facing plasmas in fusion experiments and future reactors are loaded with high fluxes (1020–1024 m−2 s−1) of H, D and T fuel particles at energies ranging from a few eV to keV. In this respect, the evolution of the radioactive T inventory in the first wall, the permeation of T through the armour into the coolant and the thermo-mechanical stability after long-term exposure are key parameters determining the applicability of a first wall material. Tungsten exhibits fast hydrogen diffusion, but an extremely low solubility limit. Due to the fast diffusion of hydrogen and the short ion range, most of the incident ions will quickly reach the surface and recycle into the plasma chamber. For steady-state operation the solute hydrogen for the typical fusion reactor geometry and wall conditions can reach an inventory of about 1 kg. However, in short-pulse operation typical of ITER, solute hydrogen will diffuse out after each pulse and the remaining inventory will consist of hydrogen trapped in lattice defects, such as dislocations, grain boundaries and irradiation-induced traps. In high-flux areas the hydrogen energies are too low to create displacement damage. However, under these conditions the solubility limit will be exceeded within the ion range and the formation of gas bubbles and stress-induced damage occurs. In addition, simultaneous neutron fluxes from the nuclear fusion reaction D(T,n)α will lead to damage in the materials and produce trapping sites for diffusing hydrogen atoms throughout the bulk. The formation and diffusive filling of these different traps will determine the evolution of the retained T inventory. This paper will concentrate on experimental evidence for the influence different trapping sites have on the hydrogen inventory in W as studied in ion beam experiments and low-temperature plasmas. Based on the extensive experimental data, models are validated and applied to estimate the contribution of different traps to the tritium inventory in future fusion reactors.