Curve squeal is an intense tonal noise occurring when a rail vehicle negotiates a sharp curve. The phenomenon can be considered to be chaotic, with a widely differing likelihood of occurrence on different days or even times of day. The term curve squeal may include several different phenomena with a wide range of dominant frequencies and potentially different excitation mechanisms. This review addresses the different squeal phenomena and the approaches used to model squeal noise; both time-domain and frequency-domain approaches are discussed and compared. Supporting measurements using test rigs and field tests are also summarised. A particular aspect that is addressed is the excitation mechanism. Two mechanisms have mainly been considered in previous publications. In many early papers the squeal was supposed to be generated by the so-called falling friction characteristic in which the friction coefficient reduces with increasing sliding velocity. More recently the mode coupling mechanism has been raised as an alternative. These two mechanisms are explained and compared and the evidence for each is discussed. Finally, a short review is given of mitigation measures and some suggestions are offered for why these are not always successful.