A great variety of experiments, like heat release measurements, acoustic measurements, and transport measurements on mesoscopic samples, have proved that two-level systems (TLSs) play a crucial role in the low-temperature thermal and electric properties of disordered systems. This paper is aimed at reviewing the role of slow TLSs in point contacts. First the theory of point contacts is summarized, concentrating on the discussion of different point-contact models, and on the different regimes of electron flow in the contact, mainly focusing on the ballistic and diffusive limit. The Boltzmann equation is solved in both regimes, and the position dependence of the electrical potential is determined. Then the scattering processes in point contacts are investigated, particularly concentrating on the scattering on slow TLSs. If the electron-assisted transitions between the two states are negligible the electron-two-level system interaction can be treated with a simplified Hamiltonian. The scattering on such slow TLSs causes non-linearity in the current-voltage characteristics of the point contact, which can be determined using Fermi's Golden Rule. These calculations are presented showing both the contribution of elastic and inelastic scattering, and including the dependence on the position of the TLS, and on the effect of high-frequency irradiation. These results are used to discuss the differences between these slow TLSs and the fast centres which may be described by the two-channel Kondo model. The available experimental results are analysed, distinguishing between the effects due to the different types of TLSs.
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