The physics of Low Energy Ion Scattering (LEIS) and its application as a surface analytical technique are reviewed. It is shown that compositional and short-range structural information can be obtained by choosing experimental conditions which optimize the contributions of single and double (or multiple) collisions, respectively. The LEIS technique allows mass analysis in a straightforward way, possesses a high surface selectivity but is unable to provide quantitative information in isolation due to scattering cross-section uncertainties and not easily quantifiable charge exchange effects. Structural information regarding adsorbate positions on single crystal surfaces and the short-range substrate structure (including damaged and reconstructed surfaces) can be obtained by exploiting shadowing and/or multiple scattering phenomena. The progress made in recent years in this area is charted. It is shown that computer simulations often play an important role in this type of study. Effects, such as charge exchange, inelastic energy loss and ion beam surface perturbations, which complicate the use of low energy ion scattering for surface analysis are discussed in detail. The present status of the technique in the different areas of study is indicated.