The study of driving behaviour has become increasingly important in the development of transport and vehicle technologies. Microscopic traffic models simulate individual driver behaviour to understand and predict traffic flow. One of the key components in microscopic simulation is the car-following (CF) model, which describes the behaviour of vehicles in terms of how they follow the vehicle in front of them. Some excellent reviews of CF models are available, however, to the best of the authors’ knowledge, none of them provides a comprehensive analysis that covers and compares different model categories including kinematics-based, dynamics-based, psychological-based, and learning-based. This paper, therefore, provides an overview of the developments and future directions of CF models, encompassing all the previously mentioned categories. It first introduces the fundamental concepts of traffic models, in particular CF models. It then reviews the progress of CF models, which are classified into the above four categories. The advantages and limitations of existing CF models are discussed. The paper further identifies several research directions for future work, including the integration of emerging vehicle technologies, the incorporation of real-world traffic data, and the calibration and validation of model parameters. It concludes by emphasizing the importance of interdisciplinary collaboration and the need for further research to improve the accuracy and practicality of CF models.