Atomic processes of ionization, recombination and electron capture in collisions of positive ions with atoms, ions, electrons and molecules are considered, as well as the influence of these processes in the interaction of ion beams with media in a wide energy range — from low to super-relativistic, but mainly at energies E ~ 10 keV/u — 100 GeV/u. The main features of effective cross sections of the processes, depending on the collision energy, atomic structure and density effects in gases, solids and plasmas, are described. The role of the dielectronic recombination in the interaction of heavy multi-electron ion beams with a plasma is considered in detail. The presented review covers experimental and theoretical achievements over the last 5—10 years in the field of accelerator physics and physics of collisions of heavy ions with atomic systems.