In many solids, heavy ions of high kinetic energy (MeV-GeV) produce long cylindrical damage trails with diameters of order 10 nm. Up to now, no information was available how solids cope with the simultaneous exposure to these energetic projectiles and to high pressure. We report the first experiments where relativistic uranium and gold ions from the SIS heavy-ion synchrotron at GSI were injected through several mm of diamond into solid samples pressurized up to 14 GPa in a diamond anvil cell. In synthetic graphite and natural zircon, the combination of pressure and ion beams triggered drastic structural changes not caused by the applied pressure or the ions alone. The modifications comprise long-range amorphization of graphite rather than individual track formation, and in the case of zircon the decomposition into nanocrystals and nucleation of the high-pressure phase reidite.