Summary: The article presents the HYPER project, a proposal for a satellite mission on precision matter-wave interferometry. For the mission several scientific objectives are under investigation, for which atom interferometers proved on ground to be a true complementary and competitive alternative for classical concepts: The application of atom interferometers as gyroscopes, the measurement of the gravitational acceleration (including tests of the universality of the free fall of atoms) and the precise determination of the fine-structure constant. The paper focuses on the use of cold-atom gyroscopes to map the Lense-Thirring effect close by the Earth and reports on results of recent feasibility studies of the European Space Agency. HYPER requires new concepts of compact, high-resolution matter-wave gyroscopes, which are better adapted to the use in satellite based experiments. The article will give a concise overview of the status and strategies in the field.