Assessing the performance of deep geological repositories for heat-generating radioactive waste requires reliable predictions of the thermo-hydro-mechanical (THM) behaviour of the clay barriers (the buffer material as well as the host rock/clay). This represents an important element of the waste isolation system. In order to provide reasonable assurance that clay barriers will ensure nuclear waste isolation, it is essential to understand their behaviour under a variety of environmental conditions. The phenomena involved are complex, and adequately understanding the constitutive behaviour of clays and modelling their evolution is challenging. The stress-strain material behaviours that need to be understood and modelled include drying and wetting in non-isothermal conditions and heating-cooling in non-saturated conditions. Other aspects should be considered, such as drying induced cracks and the role of the material structure and its multi-porosity. The difficulty of some of these tasks is increased by the fact that some effects are coupled. The fundamental behaviours of clayey materials under the considered THM conditions are first identified and highlighted for deep repository experiments. We then propose a mechanical stress-strain constitutive frame-work to model the behaviour of clay barriers. This includes aspects such as the thermo-plastic behaviour of saturated and unsaturated materials. In the third part, we show that the proposed framework allows us to ex-perimentally explain observed behaviours and to predict the THM behaviour of clay barriers.