The progress brought by the deep learning technology over the last decade has inspired many research domains, such as radar signal processing, speech and audio recognition, etc., to apply it to their respective problems. Most of the prominent deep learning models exploit data representations acquired with either Lidar or camera sensors, leaving automotive radars rarely used. This is despite the vital potential of radars in adverse weather conditions, as well as their ability to simultaneously measure an object’s range and radial velocity seamlessly. As radar signals have not been exploited very much so far, there is a lack of available benchmark data. However, recently, there has been a lot of interest in applying radar data as input to various deep learning algorithms, as more datasets are being provided. To this end, this paper presents a survey of various deep learning approaches processing radar signals to accomplish some significant tasks in an autonomous driving application, such as detection and classification. We have itemized the review based on different radar signal representations, as it is one of the critical aspects while using radar data with deep learning models. Furthermore, we give an extensive review of the recent deep learning-based multi-sensor fusion models exploiting radar signals and camera images for object detection tasks. We then provide a summary of the available datasets containing radar data. Finally, we discuss the gaps and important innovations in the reviewed papers and highlight some possible future research prospects.