A cryogenic electrostatic storage ring, the CSR, has been taken into operation at the Max Planck Institute for Nuclear Physics. With laboratory astrophysics studies as one of its goals, the machine was built to store fast ion beams in extremely high vacuum, screened against terrestrial thermal radiation, and over times reaching up to an hour. Through the few-Kelvin cryogenic environment and the extreme suppression of collisional perturbations, in contrast to other ion-trap arrangements, low-energy molecular excitations (rotation, low-frequency vibrations or isomeric conformations) can evolve freely and thermalize purely by radiation. Controlled interaction is applied to the circulating ions by laser radiation or by merged or crossed particle beams (electrons, neutral atoms). Event-by-event multi-fragment detection, even for neutral products, and the high accuracy of charged-particle current measurements enable reaction cross-section and branching ratio measurements. The presentation focuses on laboratory studies of rotational excitation in small molecular ions and on inelastic collisions of molecular ions with cold electrons (dissociative recombination and collisional (de-)excitation). First experimental results, planned studies on polyatomic species relevant in interstellar and circumstellar media, and further projects to study complex molecular ions will be addressed.