The purpose of this review is to investigate and analyze recent publications on experimental studies on mathematical models that evaluate, or suggest that such a method can be evaluated, the drying process of stored grains by aeration and how the heat transfer occurs in this process. The emphasis for this paper is on the observation of types of grains ordinarily usually used in the experimental studies, on the mathematical techniques that define the models and on the efficiency observed for these studied models. Finally, it is expected to present a paper with a synthesis consistent with the current reality that might direct subsequent research on the area of heat transfer on stored grains drying by aeration.