The framework of locally covariant field theory proved extremely fruitful for QFT on curved space-times. It can be straightforwardly generalized to more general non trivial background fields, in particular gauge connections. I will present two applications of this framework. The first is an elementary computation of the chiral anomalies, directly on Lorentzian space-times. The second is QED in external potentials, where I compare the locally covariant definition of the current to other definitions and consider it in concrete cases.