Modelling, predicting and analysing driver behaviours are essential to advanced driver assistance systems (ADAS) and the comprehensive understanding of complex driving scenarios. Recently, with the development of deep learning (DL), numerous driver behaviour learning (DBL) methods have been proposed and applied in connected vehicles (CV) and intelligent transportation systems (ITS). This study provides a review of DBL, which mainly focuses on typical applications in CV and ITS. First, a comprehensive review of the state-of-the-art DBL is presented. Next, Given the constantly changing nature of real driving scenarios, most existing learning-based models may suffer from the so-called “catastrophic forgetting,” which refers to their inability to perform well in previously learned scenarios after acquiring new ones. As a solution to the aforementioned issue, this paper presents a framework for continual driver behaviour learning (CDBL) by leveraging continual learning technology. The proposed CDBL framework is demonstrated to outperform existing methods in behaviour prediction through a case study. Finally, future works, potential challenges and emerging trends in this area are highlighted.