In this chapter we discuss a variety of issues related to the phenomenon of one-dimensional conductance quantization, probably one of the most important phenomena exhibited by mesoscopic conductors. The quantization is observed in one of the simplest of structures, namely the quantum point contact (QPC) that can be straightforwardly realized by means of the split-gate technique. The QPC is essentially a nanoscale constriction, connected at either end to macroscopic reservoirs, through which electrons may travel ballistically at low temperatures. In this chapter, we discuss how the strong lateral confinement that electrons experience as they pass through the QPC quantizes their energy into a series of discrete one-dimensional subbands. Through a simple analysis, based on a noninteracting model of transport that assumes linear response, we show that the conductance associated with these subbands takes the universal value 2e2/h, independent of the subband index. This results in the observation of a universal staircase structure in the conductance of QPCs, as their gate voltage is used to change the number of occupied subbands one at a time. An important requirement for the observation of this effect is that electron transport through the QPC should be ballistic, and we will see how this typically limits its observation to low temperatures (≤ 4.2 K). The conductance quantization provides a striking demonstration of the validity of the Landauer approach to electrical conduction, and in this chapter we also extend the discussion to consider the influence of scattering and non-vanishing source–drain bias on the conductance.