Within the last ten to fifteen years, models emerged for describing and developing undergraduate research and inquiry. This article discusses four examples of modelling didactical issues around undergraduate research and inquiry. The aim of the first part of this article is to scrutinize the epistemological and the didactical purpose of these models. As essential dimensions of undergraduate research and inquiry are neglected, two new models are developed. The first puts the coordination of theory and evidence in the centre and determines (...) three different horizons of significance in the field of science. In relation to these horizons, the second model highlights the broader societal context of scientific practices. The role of research and science in society is recognized here on the one hand as an affirmative process of institutionalization of approved knowledge, and on the other, as practices of criticizing and breaking away from established forms of knowing, testing, evaluating, and approving. Concomitantly, the education of students through and within scientific practices of research and inquiry is interpreted against the backdrop of two opposite trajectories influencing students’ ambitions to engage with problems of science. Didactics of higher education therefore need to distinguish between long-term and short-term goals. It is argued that the latter concretizes the former. This understanding of teaching is corroborated against the backdrop of the concept of learning as ‘enculturation’ in science. The argumentation refers back to insights by Lev S. Vygotsky, Ludwik Fleck and Michael Polanyi. (shrink)