We publish three Roadmaps on photonic, electronic and atomic collision physics in order to celebrate the 60th anniversary of the ICPEAC conference. Roadmap III focusses on heavy particles: with zero to relativistic speeds. Modern theoretical and experimental approaches provide detailed insight into the wide range of many-body interactions involving projectiles and targets of varying complexity ranging from simple atoms, through molecules and clusters, complex biomolecules and nanoparticles to surfaces and crystals. These developments have been driven by technological progress and future developments will expand the horizon of the systems that can be studied. This Roadmap aims at looking back along the road, explaining the evolution of the field, and looking forward, collecting nineteen contributions from leading scientists in the field.