Our purpose in this chapter is to describe an approach (often referred to as the Landauer approach) that has proved to be very useful in describing mesoscopic transport. In this approach, the current through a conductor is expressed in terms of the probability that an electron can transmit through it. The earliest application of current formulas of this type was in the calculation of the current-voltage characteristics of tunneling junctions where the transmission probability is usually much less than unity (see J. Frenkel (1930), Phys. Rev., 36, 1604 or W. Ehrenberg and H. Honl (1931), Z. Phys., 68, 289). Landauer [2.1] related the linear response conductance to the transmission probability and drew attention to the subtle questions that arise when we apply this relation to conductors having transmission probabilities close to unity. For example, if we impress a voltage across two contacts to a ballistic conductor (that is, one having a transmission probability of unity) the current is finite indicating that the resistance is not zero. But can a ballistic conductor have any resistance? If not, where does this resistance come from? These questions were clarified by Imry [2.2], enlarging upon earlier notions due to Engquist and Anderson [2.3]. Büttiker extended the approach to describe multi-terminal measurements in magnetic fields and this formulation (generally referred to as the Landauer–Büttiker formalism) has been widely used in the interpretation of mesoscopic experiments.