Combining non-equilibrium transport with spectroscopic measurements provides a unique tool for the investigation of the microscopic processes in mesoscopic conductors. Experiments on resistive quantum wires show that the non-equilibrium quasiparticle distribution function f(E,V) as a function of the quasiparticle energy E approximately obeys the scaling property, f(E,V) = f(E/V), if the transport voltage V exceeds a certain crossover scale V^*. This scaling indicates anomalous inelastic relaxation processes to be present. It is demonstrated that the latter can be induced by quantum impurities with a degenerate internal degree of freedom, i.e. by Kondo impurities. We review a perturbative renormalization group method to describe the Kondo effect in an arbitrary stationary non-equilibrium situation as well as in a magnetic field, and show that the experiments are explained in detail by a very low concentration of Kondo impurities, with V^* TK, the Kondo temperature. It is discussed how this provides a possible explanation of the observed low-temperature plateau of the decoherence time in mesoscopic conductors.