The numerical renormalization group is an inherently non-perturbative procedure, which was originally used to solve the Kondo model. The Kondo model is a simplified theoretical model which describes a system of magnetic spin-1/2 impurities which couple to metallic conduction electrons (e.g. iron impurities in gold). This problem is notoriously difficult to tackle theoretically, since perturbative techniques break down at low-energy. However, Wilson was able to prove for the first time using the numerical renormalization group that the ground state of the Kondo model is a singlet state. But perhaps more importantly, the notions of renormalization, fixed points, and renormalization group flow were introduced to the field of condensed matter theory — it is for this that Wilson won the Nobel Prize in 1982. The complete behaviour of the Kondo model, including both the high-temperature 'local moment' regime and the low-temperature 'strong coupling' regime are captured by the numerical renormalization group; an exponentially small energy scale T K (not accessible from straight perturbation theory) was shown to govern all properties at low-energies, with all physical observables such as resistivity, thermodynamics, dynamics etc. exhibiting universal scaling. This is a characteristic feature of many problems in condensed matter physics, and is a central theme of quantum impurity physics in particular. In the original example of the Kondo model, the impurity local moment is completely screened below T K by the conduction electrons via the celebrated Kondo effect ; and one famous consequence is that such materials exhibit a resistivity minimum at low temperatures, contrary to expectations based purely on the standard phonon contribution, where the resistivity is predicted to decrease monotonically with temperature.