The hygrothermal transfer is very important for the design of a building envelope for thermal comfort and economic and energy analysis of the building envelope. The applications of various materials in building envelope have been studied extensively. The study presents several models for the hygrothermal transfer for various building walls. Several energy and mass conservation equations with different boundary conditions and input considerations were presented in this paper for concrete, bricks and wooden walls. The effect of hysteresis was ignored in developing most model equations, while few considered flow pattern of fluid through the wall surfaces. Due to the flexibility of Luikov models, it formed the basis for modelling the coupled heat and mass transfer for porous material independent of hygroscopic nature with different boundary conditions defined according to the geometry and orientations. The influence of type of wall, orientation, thickness, the density of the material and climatic variations on the temperature and moisture evolutions within the building materials was more pronounced. Literature, presenting imaging models using imagery software like COMSOL multi-physics, CFD etc. were scarce considering that microscopic imagery is now deployed to measure the heat and moisture evolution in materials. Future models should include shrinkage or expansion influence on the fibrous material like wood due to their behaviour under environmental condition.