Important ideas in the modelling of trickle-bed reactors given in the literature are summarized, partly extended and placed into context which, in future, will hopefully lead to a more satisfactory theory about the important physical and chemical processes in this type of reactor. Based on the common behaviour of different reaction systems and results of previous investigations, general model equations are formulated, which seem to be applicable to many reactions in a trickle-bed reactor. A new approximation for the overall catalyst effectiveness factor-the so-called cylinder shell model-is presented, which leads to one-dimensional mass balance equations inside the catalyst for all possible values of the external wetting efficiency on a particle scale.