Supercharging has been increasingly more employed as an approach to improve the internal combustion engine (ICE) thermal efficiency. The turbocharger (TC) stands out as a well-established technology which recovers waste energy from exhaust gases to increase the ICE intake pressure and mass flow rate. Nevertheless, the increasingly stringent restrictions on greenhouse gases emission, concomitantly with performance improvement required from customers, impose a tighter pairing between TC and ICE and higher control of TC operational conditions. Matching a proper TC for a given ICE has a major importance for the global efficiency, having direct impact on specific consumption, emission levels and drivability. This process is typically performed using computational simulations via interpolations of TC tabular performance maps, which details the flow status for given shaft speed and mass flow rate. Although this method provides a reliable and accurate description of the TC performance within the mapped domain, the multiple interpolations and extrapolations required entails high computational costs. Furthermore, the extrapolations required to describe the flow outside the mapped domain are not able to predict well the actual operational condition. To circumvent these issues, alternative modelling approaches have been developed. The current paper provides a comprehensive literature review on current TC modelling strategies proposed by academics and the industry to predict the TC performance with reasonable precision and low computational cost. The review begins with a brief synopsis of TC matching and control presenting requirements and limitations. Subsequently, TC modelling is succinctly presented and its state of art for ICE simulation and control is discussed. Namely, modelling strategies evaluated in this review are physical approaches (meanline models, mean value models and non-dimensional analysis), semiphysical approaches, and black box neural networks models. Lastly, some trends and recommendations for future works are discussed.