This work addresses the problem of semantic scene understanding under dense fog. Although considerable progress has been made in semantic scene understanding, it is mainly related to clear-weather scenes. Extending recognition methods to adverse weather conditions such as fog is crucial for outdoor applications. In this paper, we propose a novel method, named Curriculum Model Adaptation (CMAda), which gradually adapts a semantic segmentation model from light synthetic fog to dense real fog in multiple steps, using both synthetic and real foggy data. In addition, we present three other main stand-alone contributions: 1) a novel method to add synthetic fog to real, clear-weather scenes using semantic input; 2) a new fog density estimator; 3) the Foggy Zurich dataset comprising 3808 real foggy images, with pixel-level semantic annotations for 16 images with dense fog. Our experiments show that 1) our fog simulation slightly outperforms a state-of-the-art competing simulation with respect to the task of semantic foggy scene understanding (SFSU); 2) CMAda improves the performance of state-of-the-art models for SFSU significantly by leveraging unlabeled real foggy data. The datasets and code will be made publicly available.