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Image restoration is a fundamental task in computer vision and machine learning, which learns a mapping between the clear images and the degraded images under various conditions (e.g., blur, low-light, haze). Yet, most existing image restoration methods are highly restricted by the requirement of degraded and clear image pairs, which limits the generalization and feasibility to enormous real-world scenarios without paired images. To address this bottleneck, we propose a Degradation-aware Dynamic Schrödinger Bridge (DDSB) for unpaired image restoration. Its general idea is to learn a Schrödinger Bridge between clear and degraded image distribution, while at the same time emphasizing the physical degradation priors to reduce the accumulation of errors during the restoration process. A Degradation-aware Optimal Transport (DOT) learning scheme is accordingly devised. Training a degradation model to learn the inverse restoration process is particularly challenging, as it must be applicable across different stages of the iterative restoration process. A Dynamic Transport with Consistency (DTC) learning objective is further proposed to reduce the loss of image details in the early iterations and therefore refine the degradation model. Extensive experiments on multiple image degradation tasks show its state-of-the-art performance over the prior arts.