Domain adaptation relaxes the assumption that test data follows the same distribution as training data in traditional machine learning. It transfers knowledge from label-rich source domain to label-scarce target domain when domain bias exists. However, most domain adaptation methods make assumptions about the relative relationship between the label space of source domain and target domain. This limits the application of these methods in reality. Therefore, universal domain adaptation is proposed to label target data without prior information of label spaces of source domain and target domain. Generally, a universal domain adaptation model needs to solve several problems. Firstly, it is desired to judge whether a target sample belongs to classes in source domain. Then it ought to transfer knowledge of common classes shared by source domain and target domain to label target samples, as well as dealing the domain bias and potential category shift. Due to its practicability, universal domain adaptation has gained more and more attention now. Many branches of it have been proposed, and researchers are trying to apply it onto datasets different from images. In this review, we conduct an exhaustive survey of universal domain adaptation methods till now from the point of problem setting and strategies. Then we compare typical methods and analyze the difficulties in the universal domain adaptation. After that, we introduce current applications of universal domain adaptation. Meanwhile, we analyze relevant research areas briefly. Lastly, we discuss problems of universal domain adaptation that can be studied further.