Storage of season-dependent agro-materials is a key process in providing food, feed and biomass throughout the whole year. We review the state of the art in physical modelling, simulation and control of ventilated bulk storage facilities, and in particular the storage of potatoes, from a state-space perspective. The basic physical relations that describe the dynamic behaviour of air and potatoes in a storage facility use laws of conservation of mass, energy and momentum and corresponding constitutive laws. However, a very complex physically based storage model is obtained if the macro climate in the air channels and the micro climate around the potato and all the interactions between air and potato are taken into consideration. Therefore, lumped, 1-D, 2-D and 3-D macro, and also some micro climate storage models were developed. These models basically focus on heat and moisture generation and transportation. The latest developments give more and more insight into the spatial distribution of the macro climate, using CFD simulation techniques. Traditionally, the indoor climate instead of the potato quality is controlled, to maintain a good product quality. However, quality control of the product can be realised if there is knowledge between the spatial distribution of temperature and moisture and the product quality. With the developments in CFD simulation, control algorithms and the state space framework, modelling and control of product quality is within reach.