Ultra-high-definition (UHD) image restoration aims to specifically solve the problem of quality degradation in ultra-high-resolution images. Recent advancements in this field are predominantly driven by deep learning-based innovations, including enhancements in dataset construction, network architecture, sampling strategies, prior knowledge integration, and loss functions. In this paper, we systematically review recent progress in UHD image restoration, covering various aspects ranging from dataset construction to algorithm design. This serves as a valuable resource for understanding state-of-the-art developments in the field. We begin by summarizing degradation models for various image restoration subproblems, such as super-resolution, low-light enhancement, deblurring, dehazing, deraining, and desnowing, and emphasizing the unique challenges of their application to UHD image restoration. We then highlight existing UHD benchmark datasets and organize the literature according to degradation types and dataset construction methods. Following this, we showcase major milestones in deep learning-driven UHD image restoration, reviewing the progression of restoration tasks, technological developments, and evaluations of existing methods. We further propose a classification framework based on network architectures and sampling strategies, helping to clearly organize existing methods. Finally, we share insights into the current research landscape and propose directions for further advancements. A related repository is available at https://github.com/wlydlut/UHD-Image-Restoration-Survey.