One of the most important maintenance costs in tramway transport comes from wear of wheel profiles. In the highly competitive railway market, the prediction of wear is then a major concern of the constructors. Four models are presented and compared, which are well adapted to tramway conditions, involving contacts on the rolling tread and on the flange with very different sliding and pressure conditions. Moreover, all models can be implemented from the natural outputs of the railway simulation packages classically used in industry for the dynamics design of the vehicles. The first one, proposed by Jendel, is based on the well-known Archard's wear model. Enblom continues Jendel's approach by taking into account the contribution of wheel deformation on the sliding velocity. The last two models, developed by Zobory, and Pearce and Sherratt, determine the wear from the energy dissipation in the contact area. The models are first compared on a theoretical basis and, for that purpose, are rewritten in a common form. Two cases are distinguished: mild wear as arising on the rolling tread and severe wear as arising on the flange. The models are also compared in the practical case of an urban transport vehicle running on circular tracks with different curve radii. Although the models show equivalent trends according to the theoretical study, important discrepancies appear between estimated wear depths. All models are actually dependent on experimental coefficients and it is likely that they were estimated in different conditions. On the other hand, a reasonable agreement can be found in some particular conditions. As an example, Zobory's, Enblom's and Jendel's models are very close to each other in severe wear conditions. It is shown that a general and reliable model could probably be developed from all positive aspects of the existing ones.