Refactoring is one of the most important activities in software engineering which is used to improve the quality of a software system. With the advancement of deep learning techniques, researchers are attempting to apply deep learning techniques to software refactoring. Consequently, dozens of deep learning-based refactoring approaches have been proposed. However, there is a lack of comprehensive reviews on such works as well as a taxonomy for deep learning-based refactoring. To this end, in this paper, we present a survey on deep learning-based software refactoring. We classify related works into five categories according to the major tasks they cover. Among these categories, we further present key aspects (i.e., code smell types, refactoring types, training strategies, and evaluation) to give insight into the details of the technologies that have supported refactoring through deep learning. The classification indicates that there is an imbalance in the adoption of deep learning techniques for the process of refactoring. Most of the deep learning techniques have been used for the detection of code smells and the recommendation of refactoring solutions as found in 56.25\% and 33.33\% of the literature respectively. In contrast, only 6.25\% and 4.17\% were towards the end-to-end code transformation as refactoring and the mining of refactorings, respectively. Notably, we found no literature representation for the quality assurance for refactoring. We also observe that most of the deep learning techniques have been used to support refactoring processes occurring at the method level whereas classes and variables attracted minimal attention. Finally, we discuss the challenges and limitations associated with the employment of deep learning-based refactorings and present some potential research opportunities for future work.