Abstract. Wind direction variability significantly affects the performance and life-time of wind turbines and wind farms. Accurately modelling wind direction variability and understanding the effects of yaw misalignment are critical towards designing better wind turbine yaw and wind farm flow controllers. This review focuses on control-oriented modelling of wind direction variability, which is an approach that aims to capture the dynamics of wind direction variability for improving controller performance over a complete set of farm flow scenarios, performing iterative controller development, and/or achieving real-time closed-loop model-based feedback control. The review covers various modelling techniques, including large eddy simulations (LES), data-driven empirical models, and machine learning models, as well as different approaches to data collection and pre-processing. The review also discusses the different challenges in modelling wind direction variability, such as data quality and availability, model uncertainty, and the trade-off between accuracy and computational cost. The review concludes with a discussion of the critical challenges which need to be overcome in control-oriented modelling of wind direction variability, including the use of both high and low-fidelity models.