Ensuring traffic safety is crucial, which necessitates the detection and prevention of road surface defects. As a result, there has been a growing interest in the literature on the subject, leading to the development of various road surface defect detection methods. The methods for detecting road defects can be categorised in various ways depending on the input data types or training methodologies. The predominant approach involves image-based methods, which analyse pixel intensities and surface textures to identify defects. Despite their popularity, image-based methods share the distinct limitation of vulnerability to weather and lighting changes. To address this issue, researchers have explored the use of additional sensors, such as laser scanners or LiDARs, providing explicit depth information to enable the detection of defects in terms of scale and volume. However, the exploration of data beyond images has not been sufficiently investigated. In this survey paper, we provide a comprehensive review of road surface defect detection studies, categorising them based on input data types and methodologies used. Additionally, we review recently proposed non-image-based methods and discuss several challenges and open problems associated with these techniques.