Monte Carlo (MC) track structure simulations follow the primary as well as all produced secondary particles in an event-by-event manner, from starting or ejection energy down to total stopping. They provide useful information on physics and chemistry of the biological response to radiation. They depend on reliable interaction cross sections and transport models of the considered radiation quality with biologically relevant materials. Most transport models focus on sufficiently fast and bare (i.e., fully ionized) ions and cross sections calculated within the (relativistic) first Born or Bethe approximations. These theories consider the projectile as a point particle and rely on proton cross sections and simple charge-scaling methods; they neglect the atomic nature of the ion and break down at low and intermediate ion energies. Heavier ions are used in particle therapy and slow to intermediate and low energies in the biologically interesting Bragg peak. Lighter and slower fragment ions, including alpha particles, protons, and neutrons are also produced in nuclear and break up reactions of charged particles. Secondary neutrons also produce recoil protons and ions, mainly in the intermediate energy range.