The main purpose of this paper is to emphasize the particularities of models needed for model-based fault detection and isolation (FDI) in contrast to the models used for control. Of special interest is the question of complexity of the model, which is of great importance for the practical implementation. This, of course, depends basically on the given situation such as the kind of plant, the measurements, the kind and number of faults to be detected and the demands for fault isolation and robustness. However, the paper shows that diagnostic models, in contrast to the wide-spread opinion that those have always to be more complex than the functional models for control, may be even less complex, because they are restricted to only those parts of the system in which the faults occur. The issue of model complexity is discussed in terms of different model-based FDI approaches analytical, knowledge-based and data-based. The ideas are illustrated in a case study, where several types of model-based FDI techniques are compared with the same plant, the amira three tank system.