Deep learning has produced state-of-the-art results for a variety of tasks. While such approaches for supervised learning have performed well, they assume that training and testing data are drawn from the same distribution, which may not always be the case. As a complement to this challenge, single-source unsupervised domain adaptation can handle situations where a network is trained on labeled data from a source domain and unlabeled data from a related but different target domain with the goal of performing well at test-time on the target domain. Many single-source and typically homogeneous unsupervised deep domain adaptation approaches have thus been developed, combining the powerful, hierarchical representations from deep learning with domain adaptation to reduce reliance on potentially-costly target data labels. This survey will compare these approaches by examining alternative methods, the unique and common elements, results, and theoretical insights. We follow this with a look at application areas and open research directions.