It is argued that knowledge about models is an important part of a profound understanding of Nature of Science. Consequently, researchers have developed different "levels of understanding" to analyse students', teachers', or experts' comprehension of this topic. In some approaches, "global" levels of understanding have been developed which mirror the idea of an understanding of models and modelling as a whole. Opposed to this, some authors have developed levels of understanding for distinct aspects concerning models and modelling in science (i.e. "aspect-dependent" levels). This points to an important issue for science education research since "global" conceptualisations might lead to less differentiated assessments and interventions than "aspect-dependent" ones. To contribute to this issue, the article summarises conceptualisations of both "global" and "aspect-dependent" levels of understanding models and modelling that have been developed in science education. Further, students' understanding of the aspects "nature of models," "multiple models," "purpose of models," "testing models," and "changing models" has been assessed (N?=?1,180; 11 to 19 years old; secondary schools; Berlin, Germany). It is discussed to what extent the data support the notion of "global" or "aspect-dependent" levels of understanding models and modelling in science. The results suggest that students seem to have a complex and at least partly inconsistent pattern of understanding models. Furthermore, students with high nonverbal intelligence and good marks seem to have a comparatively more consistent and more elaborated understanding of models and modelling than weaker students. Recommendations for assessment in science education research and teaching practice are made.