In this article we present an "instrumental approach" in mathematics education, which focuses on the interactions between students, teachers, and "artefacts." This approach analyses "mediations" attached to the use of a given artefact and "instruments" developed by the subjects from this artefact along "instrumental geneses." We draw on three "Research Cases" at university to illustrate the use of this approach: the first is about students' geneses with a programming technology; the second about students' and teachers' geneses with a virtual learning environment; and the third about textbooks and teachers professional development. We also introduce the "documentational approach," which draws on the instrumental approach, but takes into account the broader range of available "resources." It distinguishes resources and "documents" developed by teachers from these resources, and studies teachers' "documentation systems." We present a fourth "Research Case" concerning the documentation system of a mathematics teacher, and focusing on the place of technologies within this system.