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Deep learning models have achieved tremendous successes in accurate predictions for computer vision, natural language processing and speech recognition applications. However, to succeed in high-risk and safety-critical domains such as healthcare and finance, these deep learning models need to be made reliable and trustworthy. Specifically, they need to be robust and adaptive to real-world environments which can be drastically different from the training settings. In this talk, I will advocate for Bayesian principles to achieve the goal of building robust and adaptive deep learning models. I will introduce a suite of uncertainty quantification methods for Bayesian deep learning, and demonstrate applications en- abled by accurate uncertainty estimates, e.g., robust predic- tion, continual learning and repairing model failures. I will conclude by discussing the research challenges and potential impact for robust and adaptive deep learning models. This paper is part of the AAAI-23 New Faculty Highlights.