Semantic scene segmentation from a bird's-eye-view (BEV) perspective plays a crucial role in facilitating planning and decision-making for mobile robots. Although recent vision-only methods have demonstrated notable advancements in performance, they often struggle under adverse illumination conditions such as rain or nighttime. While active sensors offer a solution to this challenge, the prohibitively high cost of LiDARs remains a limiting factor. Fusing camera data with automotive radars poses a more inexpensive alternative but has received less attention in prior research. In this work, we aim to advance this promising avenue by introducing BEVCar, a novel approach for joint BEV object and map segmentation. The core novelty of our approach lies in first learning a point-based encoding of raw radar data, which is then leveraged to efficiently initialize the lifting of image features into the BEV space. We perform extensive experiments on the nuScenes dataset and demonstrate that BEVCar outperforms the current state of the art. Moreover, we show that incorporating radar information significantly enhances robustness in challenging environmental conditions and improves segmentation performance for distant objects. To foster future research, we provide the weather split of the nuScenes dataset used in our experiments, along with our code and trained models at http://bevcar.cs.uni-freiburg.de.