The review explores coupled heat and moisture transfers in bio-based and geosourced materials from experimental and numerical viewpoint. It summarizes the underlying physical phenomena, the models developed over several decades, and the resulting simulation tools up to the building scale. The article deals with an analysis of results, limitations, recent advances, and key points requiring clarification. This work emphasizes the importance of simulation software in assessing energy efficiency, preventing moisture-related issues, and ensuring occupant comfort. Various strategies, including model simplifications, model order reduction, and the use of neural networks, are presented to mitigate computation time in addressing hygrothermal issues. Additionally, standardized experimental methods for determining model input parameters are discussed, acknowledging the associated uncertainty. The establishment of a database on experimentally measured thermal performance of earth construction is also attempted. The review highlights studies comparing experimental results and simulations at the wall scale, emphasizing influential factors in hygroscopic materials such as hysteresis. Classical models are deemed less than entirely satisfactory, especially concerning moisture profiles within hygroscopic materials, but recent improvements show promise in addressing this issue. Finally, the main subjects at the building scale dealing with the hygrothermal behavior, the indoor comfort and the building energy consumption are reviewed. It underscores the limited number of studies comparing hygrothermal simulations to sensors outputs in occupied building.