Superpixels can preserve the structure and reduce the redundancy of the original image. Because of these advantages, superpixel generation or superpixel segmentation is widely used as a pre-processing step in many image processing tasks. Although superpixels can be employed to reduce computational complexity, some challenges, such as the non-Euclidean feature learning problem introduced by superpixels, still exist. This survey provides a comprehensive overview of the state-of-the-art superpixel methods, major challenges, commonly used evaluation metrics, applications of superpixels, and potential future directions for the study of superpixels. We first give a review of the state-of-the-art superpixel methods. Next, we use different evaluation metrics to evaluate the performance of 25 up-to-date superpixel methods on different datasets in different noisy environments. After that, we introduce several up-to-date applications of superpixels. Finally, we give several possible future directions for addressing the challenges of superpixels.