Wide field-of-view (FOV) cameras, which capture a larger scene area than narrow FOV cameras, are used in many applications including 3D reconstruction, autonomous driving, and video surveillance. However, wide-angle images contain distortions that violate the assumptions underlying pinhole camera models, resulting in object distortion, difficulties in estimating scene distance, area, and direction, and preventing the use of off-the-shelf deep models trained on undistorted images for downstream computer vision tasks. Image rectification, which aims to correct these distortions, can solve these problems. In this paper, we comprehensively survey progress in wide-angle image rectification from transformation models to rectification methods. Specifically, we first present a detailed description and discussion of the camera models used in different approaches. Then, we summarize several distortion models including radial distortion and projection distortion. Next, we review both traditional geometry-based image rectification methods and deep learning-based methods, where the former formulate distortion parameter estimation as an optimization problem and the latter treat it as a regression problem by leveraging the power of deep neural networks. We evaluate the performance of state-of-the-art methods on public datasets and show that although both kinds of methods can achieve good results, these methods only work well for specific camera models and distortion types. We also provide a strong baseline model and carry out an empirical study of different distortion models on synthetic datasets and real-world wide-angle images. Finally, we discuss several potential research directions that are expected to further advance this area in the future.