The present article reviews the state of our knowledge regarding the model representation of catalytic fixed-bed reactors. The first part deals with the important types of reactors and the essential factors for their qualitative interpretation. The second part is concerned with the quantitative description of processes in catalytic fixed-bed reactors with the aid of mathematical models. It is shown how the models reproduce problems typical for these reactors : "hot spot", instability region, occurrence of multiple stationary states. The extent to which the data for reactors operated under industrial reaction conditions can be improved liy refinement of the models is also examined.