Out-of-roundness in railway wheels, in particular polygonal wear resulting in regular, multi-lobed, out-of-round wheels, has become a significant problem in recent years. It is of concern to railway operators due to the increased noise and vibration it can cause. This polygonisation is caused by cyclic wear but the exact mechanism leading to this type of wear is not fully understood. It appears to be the result of dynamic linking between a resonance or other periodic excitation in the coupled vehicle–track system and the existing wear at the wheel. This paper reviews the developing body of research being carried out in many countries by research groups, manufacturers and operators. Some examples of polygonisation on different types of railway vehicles are reported including feight trains, urban transit trains and high-speed trains. The main theories for the formation mechanisms are presented and the current measurement methods, computer simulation techniques and the effects and potential mitigation methods are reviewed. In parallel, the mechanisms and consequences of discrete wheel tread irregularities, such as wheel flats and material fall-out due to rolling contact fatigue cracking, are addressed.