Deep neural networks (DNNs) have proven their capabilities in the past years and play a significant role in environment perception for the challenging application of automated driving. They are employed for tasks such as detection, semantic segmentation, and sensor fusion. Despite tremendous research efforts, several issues still need to be addressed that limit the applicability of DNNs in automated driving. The bad generalization of DNNs to unseen domains is a major problem on the way to a safe, large-scale application, because manual annotation of new domains is costly, particularly for semantic segmentation. For this reason, methods are required to adapt DNNs to new domains without labeling effort. This task is termed unsupervised domain adaptation (UDA). While several different domain shifts challenge DNNs, the shift between synthetic and real data is of particular importance for automated driving, as it allows the use of simulation environments for DNN training. We present an overview of the current state of the art in this research field. We categorize and explain the different approaches for UDA. The number of considered publications is larger than any other survey on this topic. We also go far beyond the description of the UDA state-of-the-art, as we present a quantitative comparison of approaches and point out the latest trends in this field. We conduct a critical analysis of the state-of-the-art and highlight promising future research directions. With this survey, we aim to facilitate UDA research further and encourage scientists to exploit novel research directions.