Image restoration is a family of inverse problems for recovering high quality images from corrupted observations. They are fundamental problems in image science, and they also provide a testbed for more general inverse problems. As the advances in imaging modalities, the observations trend to being with low-cost data acquisition and the image restoration problems trend to be high-scale. The image restoration is thereby still a popular topic in image science and computational mathematics. In this talk, I will introduce some traditional methods computational methods and recent learnable methods for image restoration， and finally I will also present our recent results for some medical image reconstruction problems, phase retrieval, and some other nonlinear image restoration problems.