In this talk I will present the experimental program of FAIR (Facility for Antiprotons and Ion research), a new international facility that is being constructed in Darmstadt (Germany). FAIR will provide high-energy, precisely tailored beams of antiprotons and ions at unprecedented quality and intensities. The scientific programme at FAIR covers a broad range of physics, mostly related to hadron, baryionic matter, nuclear physics and nuclear applications. I will mainly concentrate on the Nuclear Structure and Astrophysics Research Programme (NUSTAR), the part of FAIR that focuses on the production and exploitation of beams of radioactive exotic nuclei produced in fragmentation reactions. Some of these rare isotopes, although existing only for a fleeting moment, play a critical role in nuclear reactions that build up the elements in the stars and explain the abundance of chemical elements in our World. This will be used as a running example of how useful it will be to be able to carry out experiments with beams of short-lived, exotic ions. I will also mention the experimental nuclear physics community in Spain and their efforts contributing to the experimental programme of NUSTAR.