The paper gives an outline of existing modelling capabilities as well as an overview of current developments in integral modelling of hygrothermal conditions for whole buildings as presented within IEA Annex 41. Such models deal with the heat, air and moisture conditions of most relevant elements of buildings: The indoor air, the building envelope, inside constructions and furnishing. These building elements interact with each other and they are influenced by the use of the building, the building services, and the outside climate. The transport processes for heat, air and moisture also interact with each other, and everything has an impact on the energy consumption of the building and the quality of indoor air. A suite of Common Exercises for computational modelling are developed and executed within this modelling subtask. The common exercises test the current capabilities of existing models and, very importantly, they stimulate the development of new models or the expansion of capabilities of existing models. The first two Common Exercises have been executed already. Some further plans for the subsequent Common Exercises will be outlined in the paper.