© 2020 Elsevier Ltd Geomaterials exhibit elastoplastic behaviour during dynamic and repeated loading conditions. These loads are induced by the passage of a train or vehicle which then generates recoverable (resilient) deformation and/or permanent (plastic) deformation. Modelling this behaviour is still a challenge for geotechnical engineers as it implies the understanding of the complex deformation mechanism and application of advanced constitutive models. This paper reviews on the major causes of permanent deformation and the factors that influence the long-term performance of materials. It will also present the fundamental concepts of permanent deformation as well as the models and approaches used to characterise this behaviour, including: elastoplastic models, shakedown theory and mechanistic-empirical permanent deformation models. This paper will focus on the mechanistic-empirical approach and highlight the evolution of the models, and the main similarities and differences between them. A comparison between several empirical models as well as the materials used to develop the models is also discussed. These materials are compared by considering the reference conditions on the type of material and its physical state. This approach allows for an understanding of which properties can influence the performance of railway subgrade and pavement structures, as well as the main variables used to characterise this particular behaviour. An innovative ranking of geomaterials that relate to the expected permanent deformation and classification (UIC and ASTM) of soil is also discussed because it can be used as an important tool for the design process.