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We address the problem of semantic nighttime image segmentation and improve the state-of-the-art, by adapting daytime models to nighttime without using nighttime annotations. Moreover, we design a new evaluation framework to address the substantial uncertainty of semantics in nighttime images. Our central contributions are: 1) a curriculum framework to gradually adapt semantic segmentation models from day to night through progressively darker times of day, exploiting cross-time-of-day correspondences between daytime images from a reference map and dark images to guide the label inference in the dark domains; 2) a novel uncertainty-aware annotation and evaluation framework and metric for semantic segmentation, including image regions beyond human recognition capability in the evaluation in a principled fashion; 3) the Dark Zurich dataset, comprising 2416 unlabeled nighttime and 2920 unlabeled twilight images with correspondences to their daytime counterparts plus a set of 201 nighttime images with fine pixel-level annotations created with our protocol, which serves as a first benchmark for our novel evaluation. Experiments show that our map-guided curriculum adaptation significantly outperforms state-of-the-art methods on nighttime sets both for standard metrics and our uncertainty-aware metric. Furthermore, our uncertainty-aware evaluation reveals that selective invalidation of predictions can improve results on data with ambiguous content such as our benchmark and profit safety-oriented applications involving invalid inputs.