Automatic road anomaly detection and recognition systems are essential due to their effect on the comfort and safety of drivers and passengers. Drivers should be aware of bad road conditions and the existence of anomalies in routes to avoid accidents, reduce the possibility of car malfunction, and take the most appropriate route to their destinations. This led to increased research interest in automatically detecting and recognising road anomalies. The related studies can be categorised into accelerometer-based techniques and vision-based techniques. In both techniques, deep learning and mathematical methods have been utilised. This paper reviews the latest research in the anomaly detection and classification field. Several types of road anomalies are discussed, such as potholes, cracks, and speed bumps. Additionally, road damage detection techniques are used for different types of road anomalies, challenges, and limitations of current research.