In this chapter we present the basic mechanisms of ion acceleration driven by laser-plasma interaction. In “Coulomb explosion”, ions are accelerated by their own-generated electrostatic field when all electrons are removed from the target volume. In sheath acceleration, ions are accelerated by a space-charge field created at a target-vacuum interface by warm electrons. Radiation pressure acceleration occurs due to the transfer of laser pulse momentum to the the target either in thick targets (“hole boring”) or thin targets (“light sail”); the relativistic regime and the onset of instability is also discussed. A final discussion on the cooperation of basic mechanisms in experimental scenarios is given.