Astrophysical ices are exposed to different radiation fields including photons, electrons and ions. The latter stem from interstellar cosmic rays (CR), the solar and stellar winds, shock waves or are trapped in the magnetospheres of giant planets. We briefly discuss the physics of energy deposition by ion ir radiation in condensed matter and experimental methods to study the induced effects. We then present results on radiation effects such as sputtering, amorphisation and compaction, dissociation of molecules, formation of new molecular species after radiolysis and by implantation of ions. The formation and radio-resistance of organic molecules, related to the question of the initial conditions for the emergence of life, are briefly discussed. This review is not meant to be comprehensive, but rather focusses on recent findings, with special emphasis on experiments with heavy multiply charged ion beams. These experiments aim in particular at simulating the effects of CRs on icy grains in dense molecular clouds, and on the formation of molecules on icy bodies in the Solar System.