As a novel paradigm in machine learning, deep transfer learning (DTL) can harness the strengths of deep learning for feature representation, while also capitalizing on the advantages of transfer learning for knowledge transfer. Hence, DTL can effectively enhance the robustness and applicability of the data-driven RUL prediction methods, and has garnered extensive development and research attention in machinery RUL prediction. Although there are numerous systematic review articles published on the topic of the DTL-based approaches, a comprehensive overview of the application of DTL in the RUL prediction for different mechanical equipment has yet to be systematically conducted. Therefore, it is imperative to further review the pertinent literature on DTL-based approaches. This will facilitate researchers in comprehending the latest technological advancements and devising efficient solutions to address the cross-domain RUL prediction challenge. In this review, a brief overview of the theoretical background of DTL and its application in RUL prediction tasks are provided at first. Then, a detailed discussion of the primary DTL methods and their recent advancements in cross-domain RUL prediction is presented. Next, the practical application of the current research is discussed in relation to the research object and its open-source data. More importantly, several challenges and further trend are further presented to conclude this paper in the end. We have reason to hope this work can offer convenience and inspiration to researchers seeking to advance in the field of RUL prediction.