This literature survey discusses the state-of-the-art in research on why out-of-round railway wheels are developed and on the damage they cause to track and vehicle components. Although the term out-of-round wheels can be attributed to a large spectrum of different wheel defects, the focus here is on out-of-round wheels with long wavelengths, such as the so-called polygonalization with 1-5 harmonics (wavelengths) around the wheel circumference. Topics dealt with in the survey include experimental detection of wheel/rail impact loads, mathematical models to predict the development and consequences of out-of-round wheels, criteria for removal of out-of-round wheels and suggestions on how to reduce the development of out-of-round wheels.