Railway noise and ground-borne vibration induced by wheel–rail impact loads are generated by discrete wheel/rail surface irregularities or local deviations in the nominal wheel–rail contact geometry. On the running surface of a rail, a discrete irregularity can be inherent to the railway design, for example at crossings or insulated joints. On the wheel or rail, the irregularity could also be the result of surface damage due to rolling contact fatigue cracking or a consequence of wheel sliding without rolling. This review describes the mechanisms of wheel–rail impact generated by wheel flats, rail joints and crossings. These can be a source of locally increased noise and vibration levels and increased annoyance, as well as of damage to vehicle and track components. The wheel–rail excitation at such irregularities, as indicated by the vertical wheel centre trajectory, leads to an abrupt change of momentum, potentially causing a momentary loss of wheel–rail contact followed by an impact on the rail. The resulting loading is a transient and often periodically repeated event exciting vibration in a wide frequency range with most of the energy concentrated below about 1 kHz. For the numerical prediction of high-magnitude transient loading and situations potentially leading to loss of contact, a non-linear wheel–rail contact model is required, implying that the simulation of contact force is carried out in the time domain. To avoid the need for large, computationally expensive models, a hybrid approach has been developed in which the time history of the contact force is transformed into an equivalent roughness spectrum; this is used as input to frequency-domain models for the prediction of noise and vibration. Since the excitation mechanism is similar to that for rolling noise, the same types of measures to mitigate wheel and track vibration can be applied. However, the main priority should be to control the irregularity by design and regular maintenance.