The interaction of ion beams with solids and solid surfaces is described, over a wide range of energies, by classical trajectories. At low energies the elastic interaction between the ions and target atoms is important in determining the end of the trajectory, radiation damage and sputtering. The inelastic interaction, i.e. elementary excitations of the solid and ionization of target and projectile atoms, is relevant for the electronic stopping power, and hence the range of fast particles, and it is the cause of radiation damage in insulators and biological material. Applications of ion beams are surface analysis, sputtering, ion implantation and ion-beam modified thin-film growth.