A review is given on single-electron mechanisms, which dominate the electronic energy transfer processes of light ions in gases and solids. In the case of gas targets, it will be shown that it is possible to perform highly accurate ab-initio stopping power calculations which cover the range of incident energies from a few eV/u up to the Bethe regime. First principle calculations are applied to the stopping of p, H+, H0, He2+and Li3+in H and He gas targets. The resulting discrepancies to experimental data are about 10% or less and can be attributed to two-electron processes. Strong deviations from the usually assumed velocity proportionality at low incident energies as well as pronounced Z1dependencies are found and will be discussed. Furthermore, it will be shown that neither a single-harmonic-oscillator model nor local-density electron-gas approaches allow for a reliable prediction of the impact parameter dependence of the mean energy transfer. In the case of solids, perturbation theory is applied to the stopping of low energy ions in alkaline metals. These calculations include Bloch wavefunctions of Wigner-Seitz type obtained from a Hartree-Fock-Slater calculation and allow for a prediction of the mean energy loss under channelling conditions. Results of the most widely used free-electron gas approximation will be compared to data of our more complete treatment. Additionally, simple scaling laws for the stopping of light ions in gases and solids may be extracted from our results.