An external magnetic field can actually enhance superconductivity, pro vided it is strong enough. If only few lowest Landau levels are occupied, the quasi 1D nature of the electronic motion leads to an enhancement of transition temperature. The orbital frustration of the order parameter is much simplified in this limit. This limit of superconductivity, of great interest in itself, can also be used as a starting point to study orbital frustration in familiar, “low-field”, strongly type II superconductors. I briefly review some of the characteristics of superconductivity in high magnetic fields.