Interactions between the plasma and the vessel walls constitute a major engineering problem for next step fusion devices, such as ITER, determining the choice of the plasma-facing materials. A prominent issue in this choice is the tritium inventory build-up in the vessel, which must be limited for safety reasons. The initial material selection, i.e. beryllium (Be) on the main vessel walls, tungsten (W) on the divertor upper baffle and dome, and carbon fibre composite around the strike points on the divertor plates, results both from the attempt to reduce the tritium inventory and to optimize the lifetime of the plasma-facing components.In the framework of the EU Task Force on Plasma–Wall Interaction (PWI TF), the many physics aspects governing the tritium inventory are brought together. Together with supporting information from international experts represented by the ITPA SOL/DIV section, this paper describes the present status of knowledge of the in-vessel tritium inventory build-up. Firstly, the main results from present fusion devices in this field are briefly reviewed. Then, the processes involved are discussed: implantation, trapping and diffusion in plasma-facing materials are considered as well as surface erosion and co-deposition of tritium with eroded material. The intermixing of the different materials and its influence on hydrogen retention and co-deposition is a major source of uncertainty on present estimates and is also addressed.Based on the previous considerations, estimates for the tritium inventory build-up are given for the initial choice of ITER materials, as well as for alternative options. Present estimates indicate a build-up of the tritium inventory to the administrative limit within a few hundred nominal full power D : T discharges, co-deposition with carbon being the dominant process. Therefore, tritium removal methods are also an active area of research within the EU PWI TF, and are discussed. An integrated operational scheme to slow the rate of tritium accumulation is presented, which includes plasma operation as well as conditioning procedures.