Models and modeling are a major issue in science studies and in science education. In addressing such an issue, we first propose an epistemological discussion based on the works of Cartwright (1983, 1999), Fleck (1935/1979), and Hacking (1983). This leads us to emphasize the transitions between the abstract and the concrete in the modeling process, by using the notions of "nomogical machine" (Cartwright, 1999), "language game" (Wittgenstein, 1953/1997), and "thought style" (Fleck, 1935/1979). Then, in the light of our epistemological approach, we study four cases coming from the implementations of research-based design activities (SESAMES, 2007). These four case studies illustrate how students are engaged in constructing relations between the abstract and the concrete through modeling activities, by elaborating at the same time specific language games and appropriate thought styles. Finally, we draw some implications for science teaching. It is suggested that considering "didactic" nomological machines as embedding knowledge on the one hand, and classes as thought collectives, on the other hand, may relevantly contribute to science education and science education research. (Contains 5 figures.)