In line with the development of Industry 4.0, more and more attention is attracted to the field of surface defect detection. Improving efficiency as well as saving labor costs has steadily become a matter of great concern in industry field, where deep learning-based algorithms performs better than traditional vision inspection methods in recent years. While existing deep learning-based algorithms are biased towards supervised learning, which not only necessitates a huge amount of labeled data and a significant amount of labor, but it is also inefficient and has certain limitations. In contrast, recent research shows that unsupervised learning has great potential in tackling above disadvantages for visual anomaly detection. In this survey, we summarize current challenges and provide a thorough overview of recently proposed unsupervised algorithms for visual anomaly detection covering five categories, whose innovation points and frameworks are described in detail. Meanwhile, information on publicly available datasets containing surface image samples are provided. By comparing different classes of methods, the advantages and disadvantages of anomaly detection algorithms are summarized. It is expected to assist both the research community and industry in developing a broader and cross-domain perspective.