Since lithium-containing ceramics (e.g. Li2O, LiAlO2, Li4SiO4, Li2ZrO3, Li2TiO3) are considered as breeding materials in the blanket of the next generation fusion reactors, several studies are in progress to evaluate their behaviour under irradiation in both operating and accidental conditions. Based on safety and economic considerations tritium inventory and release are the most critical issues for blanket concept. Investigation of tritium transport processes by using comprehensive physical-mathematical models is one of the current activities in this area. Although some analytical models and numerical methods dealing with tritium transport and release in fine-grained ceramic were already developed and applied to interpret results from in-situ and/or post-irradiation annealing experiments, it is necessary that presently available computer codes enlarge their range of applicability to be able to predict, with increased accuracy, the tritium release response for a wider range of experimental conditions and material characteristics. This paper reviews the tritium modelling activity and summarizes the existing transport models and computer codes highlighting models development and focusing on major changes and evolutionary improvements.1 Validation of models by comparison of calculated results with experimental ones is also reported and discussed. Areas of future applications are identified and emphasis is placed upon the growing need of developing more accurate computer codes with the aim to improve the accuracy of blanket tritium inventory estimations.