Deep disposal of high-level radioactive waste is the preferred solution worldwide for the long-term disposal of nuclear waste. This concept involves a series of geological and engineered barriers that provide isolation of the waste from the biosphere. Most designs involve bentonite clays as seals in different forms. During the operation of the repository, the bentonite will be subjected to a series of complex thermo-hydro-mechanical phenomena that will interact with each other. Predicting the long-term safety of geological repositories thus involve a rigorous analysis of these multi-physical processes. This paper presents a review of recent numerical approaches and analyses that have aimed to improve the understanding of processes that will take place in clay barriers over the lifetime of nuclear waste repositories. The understanding of bentonite behavior from laboratory experiments under relevant conditions is analyzed. Constitutive models that attempt to predict such behavior are presented, focusing on the stress-strain model ACMEG-TS. These models are implemented in the finite element code Lagamine which allows for the study of real scale tests. Two application cases are presented: the performance of a clay barrier according to the Swiss design, and a model of the FEEBX in situ experiment, which was modelled after a real repository under natural conditions. Overall, the relevant processes are well captured quantitatively by the models, allowing for the establishment of sound basis for future prediction and long-term design of the final underground repositories.