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Unsupervised domain adaptation (UDA) aims to adapt a model trained on the source domain (e.g. synthetic data) to the target domain (e.g. real-world data) without requiring further annotations on the target domain. This work focuses on UDA for semantic segmentation as real-world pixel-wise annotations are particularly expensive to acquire. As UDA methods for semantic segmentation are usually GPU memory intensive, most previous methods operate only on downscaled images. We question this design as low-resolution predictions often fail to preserve fine details. The alternative of training with random crops of high-resolution images alleviates this problem but falls short in capturing long-range, domain-robust context information. Therefore, we propose HRDA, a multi-resolution training approach for UDA, that combines the strengths of small high-resolution crops to preserve fine segmentation details and large low-resolution crops to capture long-range context dependencies with a learned scale attention, while maintaining a manageable GPU memory footprint. HRDA enables adapting small objects and preserving fine segmentation details. It significantly improves the state-of-the-art performance by 5.5 mIoU for GTA-to-Cityscapes and 4.9 mIoU for Synthia-to-Cityscapes, resulting in unprecedented 73.8 and 65.8 mIoU, respectively. The implementation is available at https://github.com/lhoyer/HRDA.