Abstract : A phenomenological description of one-electron transfer leading to ion neutralization in ion-surface scattering is summarized. A perturbative treatment using an effective interaction in the Anderson-Newns Hamiltonian is then reviewed, and tje conditions under which the perturbative series has fast convergence are explored in terms of the electronic and dynamical properties of the collision system. Calculational results are discussed for proton neutralization at different alkali-halide surfaces. In the case of negative-ion formation and hence two-electron transfer to the incoming projectile ion, the Anderson correlation energy U is included in the analysis. Calculations of the probability of negative-ion formation are in qualitative agreement with experiments on the conversion of H+ (D+) to H- (D-) by scattering from a cesiated W(110) surface. The interplay between temperature effects and U are discussed. Improvements on the calculations by incorporating the image potential into the ionic energy level shift are considered. Keywords include: ION-SURFACE Scattering, Electron Transfer, Anderson-Newns Hamiltonian, Proton Neutralization, Negative-ion Formation, Correlation Energy.