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As AI systems have obtained significant performance to be deployed widely in our daily live and human society, people both enjoy the benefits brought by these technologies and suffer many social issues induced by these systems. To make AI systems good enough and trustworthy, plenty of researches have been done to build guidelines for trustworthy AI systems. Machine learning is one of the most important parts for AI systems and representation learning is the fundamental technology in machine learning. How to make the representation learning trustworthy in real-world application, e.g., cross domain scenarios, is very valuable and necessary for both machine learning and AI system fields. Inspired by the concepts in trustworthy AI, we proposed the first trustworthy representation learning across domains framework which includes four concepts, i.e, robustness, privacy, fairness, and explainability, to give a comprehensive literature review on this research direction. Specifically, we first introduce the details of the proposed trustworthy framework for representation learning across domains. Second, we provide basic notions and comprehensively summarize existing methods for the trustworthy framework from four concepts. Finally, we conclude this survey with insights and discussions on future research directions.