The book reviews the progress achieved over the last decade in the study of collisions between an ion and an atom in which both the atomic particles carry electrons and can undergo transitions between their internal states - including continua. It presents the detailed considerations of different theoretical approaches that can be used to describe collisions of structured atomic particles for the very broad interval of impact energies ranging from 0.5-1 MeV/u till extreme relativistic energies where the collision velocity very closely approaches the speed of light.