We review the non-perturbative theoretical framework set up recently to compute the inelastic scattering cross section from quantum impurities [G. Zar
xe1;nd, L. Borda, J. von Delft and N. Andrei, Phys. Rev. Lett. 93 (2004) 107204] and show how it can be applied to a number of quantum impurity models. We first use this method for the
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single-channel Kondo model and the
Anderson model. In both cases, a large plateau is found in the inelastic scattering rate for incoming energies above
TK, and a quasilinear regime appears in the energy range
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, in agreement with the experimental observations. We also present results for the 2-channel Kondo model, the prototype of all non-Fermi liquid models, and show that there half of the scattering remains inelastic even at the Fermi energy.