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With the rapid advancements of sensor technology and deep learning, autonomous driving systems are providing safe and efficient access to intelligent vehicles as well as intelligent transportation. Among these equipped sensors, the radar sensor plays a crucial role in providing robust perception information in diverse environmental conditions. This review focuses on exploring different radar data representations utilized in autonomous driving systems. Firstly, we introduce the capabilities and limitations of the radar sensor by examining the working principles of radar perception and signal processing of radar measurements. Then, we delve into the generation process of five radar representations, including the ADC signal, radar tensor, point cloud, grid map, and micro-Doppler signature. For each radar representation, we examine the related datasets, methods, advantages and limitations. Furthermore, we discuss the challenges faced in these data representations and propose potential research directions. Above all, this comprehensive review offers an in-depth insight into how these representations enhance autonomous system capabilities, providing guidance for radar perception researchers. To facilitate retrieval and comparison of different data representations, datasets and methods, we provide an interactive website at https://radar-camera-fusion.github.io/radar.